I found this question on Stackexchange and posted a response to it. I copy my response below because I believe it is important to understand how thoughts developed during the Arian Controversy.
The question correctly stated that when people talk about “the Nicene Creed,” they often mean the creed formulated at the Council of Constantinople in AD 381.
But the question also quoted Britannica, saying that the Niceno-Constantinopolitan Creed of 381 “was probably … an independent document and not an enlargement of the Creed of Nicaea.“
My Answer
The Arian Controversy
As the other answers already indicate, the description of the Son as homoousion (of the same substance) with the Father, is found for the first time in the Nicene Creed of 325. After Nicaea followed a period of intense controversy. As indicated by the following names of the sides in that controversy, the dispute was not about the entire creed, but specifically about the word homoousion:
Homoousian = Same Substance,
Homoiousian = Similar Substance,
Heteroousian = Different Substance,
Homoian = In this view, we should not talk about God’s substance because that is not revealed in the Scriptures.
(See the Wikipedia page on the Arian Controversy for more detail.)
Since that same controversial and unscriptural word appears in the creed of 381, that creed was an update of the 325-creed. As the question also noted, the Wikipedia page on the Nicene Creed compares the two creeds and shows huge similarities.
However, rather than saying that Britannica is wrong, I propose we understand the quote from Britannica differently. To explain:
Confounded the confusion
The 325-creed was formulated near the beginning of the Arian Controversy but it only served to increase the confusion:
“The creed of Nicaea, sanctioned by imperial decree … only added increased confusion and complication to the problem it was intended to solve.” (Boyd, p38)
“The Creed of Nicaea of 325, produced in order to end the controversy, signally failed to do so. Indeed, it ultimately confounded the confusion because its use of the words ousia and hypostasis was so ambiguous as to suggest that the Fathers of Nicaea had fallen into Sabellianism, a view recognized as heresy even at that period.” (Hanson)
50 Year Arian Controversy
This resulted, then, in that huge controversy for the next 50 years when the church rejected the Nicene Creed and proposed various alternatives. For example:
“A string of councils began to be called in which the formula of Nicaea was called into question and even drastically modified.” (Steven Wedgeworth)
“In 357 a council held in Sirmium in Illyria forbade the use of ousia (nature) in speaking of the relationship between the Father and the Son. With this, the homoousios of Nicaea became a dead confession.” (A Short History of the Early Church, Harry R. Boer, p117)
That 357-creed stated:
“No one can doubt that the Father is greater in honor and dignity and Godhead, and in the very name of Father, the Son Himself testifying, ‘The Father that sent me is greater than I’ (John 10:29, 14:28) … the Father is greater, and the Son subordinated to the Father.”
At another council at Seleucia in 359, the majority accepted a “similar substance” (Homo-i-ousian) creed, saying that the substance of the Son is similar to the substance of the Father.
But emperor Constantius requested a third council, at Constantinople, of both the eastern and western bishops, to resolve the split at Seleucia. At first, that council accepted a Heteroousion (different substance) creed, but after the emperor exiled some of the leaders of that view, the council reverted to a homoian creed.
My point is that, during that 50-year period, while the Nicene Creed was rejected by the church, Athanasius kept on working vigorously in defense of the Nicene Creed. At the end of his life, his cause was taken up by the three Cappadocian fathers, who were all born after the Nicene Creed of 325 was formulated. However, they did more than just to defend the Nicene Creed. Rather, they developed new theories.
Firstly, they redefined the word hypostasis in order to deal with the confusion caused by the Nicene Creed:
“It was mainly under the influence of the Cappadocian Fathers that the terminology was clarified and standardized so that the formula “three hypostases in one ousia” came to be accepted as an epitome of the orthodox doctrine of the Trinity.” (González, Justo L. (1987). A History of Christian Thought: From the Beginnings to the Council of Chalcedon. p. 307.) (Hypostasis)
They also developed the view of the Holy Spirit that was taken up in the 381-creed. The HarperCollins Encyclopedia of Catholicism, “God,” p. 568, states that the teaching of the three Cappadocian Fathers “made it possible for the Council of Constantinople (381) to affirm the divinity of the Holy Spirit, which up to that point had nowhere been clearly stated, not even in Scripture.”
Proposal
I propose, therefore, that although the creed of 381 reads very similar to the creed of 325, we understand the Brittanica-statement to say that the Arian Controversy stimulated a huge jump in the development of the Trinity doctrine and that, what the authors of the 381 creed meant by that creed is significantly different from what the authors of the 325 creed meant.
In the fourth century, various theories of the ontology (nature) of Christ competed for domination in the church. Commentators often describe this as a dispute between the Nicene Creed and Arianism, but this reflects a superficial understanding of the situation. For example:
(1) The article on the Nicene Creed shows that this decree describes Christ as subordinate to the Father. And since the term Arianism is often understood to refer to any theory that this is contrary to the Trinity doctrine, in which Christ is co-equal with the Father, the Nicene Creed may also be regarded as Arianism.
(2) The term Arianism comes from the name of Arius, a priest from Alexandria in the fourth century, whose dispute with his bishop Alexander spraked the Arian Controversy. During the 55 years after Arius’ teachings were rejected by the Nicene council, various theories of the nature of Christ prevailed that were different from both Arius’s teachings and the Trinity doctrine.
A more precise delineation of these competing theories is as follows:
Same Substance
The Council of Nicene in 325 agreed that Christ is Homoousion “of the same substance” as the Father. , was by and later ratified by the First Council of Constantinople (381).
Like the Father
In July 359, the Council of Ariminum concluded that the Son was “like the Father,” without reference to substance. In this view, the Bible does not reveal whether the Son is of the same substance as the Father and we, therefore, should not speculate about such things. See Homoian or Homoeanism.
Similar in Substance
The council of Seleucia agreed in 359 that the Son was “similar in substance” to the Father but not necessarily of the “same substance,” as the Nicene Creed. See Homoiousian or Arian controversy.
Dissimilar Substance
The council of Constantinople in 359 at first accepted that the substance of the Son was “dissimilar” from that of the Father. See Heteroousian or Arian controversy. This is similar to what Arius taught.
One Substance
It is possible to compare this list of theories to the teaching that the Son was “of one substance” with the Father. This is a refinement and further development of the “same substance” concept of the Nicene Creed. While “same substance” may be understood as that the Father and Son have the same substance like people have the same substance, “one substance” implies that they share one common substance; like two Persons in one body or being, as in the Trinity doctrine, where the Father and Son are three Persons in one Being.
Trinity Doctrine
The Nicene Creed (325) and the Creed of Constantinople (381) form the basis of the Trinity Doctrine, but the language of three distinct and infinite hypostases, or divine persons, the Father, the Son, and the Holy Spirit, that possess the very same (numerically the same, as opposed to qualitatively the same) divine ousia, only became universally accepted after the First Council of Constantinople in AD 381. (See, Homoousion – Wikipedia or Lienhard, Joseph T. Ousia and Hypostasis.)
The Trinity Doctrine was only fully formulated in the Athanasian Creed from the late fifth or early sixth century.
Conclusion
The point is this: This article shows that Emperor Theodosius I, when he came to power, crushed Arianism. However, what he really crushed was all resistance to the teaching of the Nicene Creed that the Father and Son have the same ousia.
Summary of this article
Constantine had a decisive influence on the formulation of the Nicene Creed but later rejected the Homoousion Christology of the Nicene Creed. The emperors who succeeded Constantine crushed the church leaders who taught the homoousion principle in the Nicene Creed. When emperor Valens died in 378, the imperial capital was solidly Arian. Theodosius I succeeded Valens. He was a passionate supporter of Homoousion Christology. Commentators often refer to the Council of Constantinople of 381 as the turning point where Arianism was replaced by Nicene Christology, but that council was a mere formality. Already prior to the council, Theodosius outlawed all other forms of Christianity and exiled Arian bishops (Theodosian Code 16:2, 1 Friell, G., Williams, S., Theodosius: The Empire at Bay, London, 1994 – See, Homoousion – Wikipedia). Furthermore, Arians were not allowed to attend the Council of 381.
The 381 Council, therefore, was simply a formality. The real decisions were taken by the Roman Emperor. Theodosius, with the strong arm of the empire, effectively wiped out Arianism among the ruling class and elite of the Eastern Empire. This supports again the main thesis of this article series, namely that the emperors had a decisive influence on the Christology of the church.
The 381 Creed does not contain the Trinity concept, namely that the Father, Son and Holy Spirit are three Persons with three minds or wills in one Being. But Theodosius’ Edict of Thessalonica of 380 does prescribe Trinitarian theology. In other words, the State laws were Trinitarian while the church decreed lagged behind. This also supports the thesis that the Christology of the church was determined by the emperors.
In the centuries after Theodosius, the church formulated the doctrines that Christ had two separate natures, namely that He had both a divine and a human nature, and that Mary is the Mother of God.
As discussed in the article on Fourth Century Arianism, Constantine had a decisive influence on the formulation of the Nicene Creed. He forced the Council of Nicaea to accept the key term Homoousios and to condemn Arianism. However, just a few years later, Constantine reversed his position, banished the main promotor of the Nicene Creed (Athanasius), and allowed the Arian bishops who were exiled after Nicaea, to return.
Constantine’s son and successor, Constantius II, was openly Arian. At first, Constantius only ruled in the east but, by the year 353, he became the sole ruler of the empire. He crushed the Nicene party, forcing the western bishops to abandon Athanasius and exiled leaders of the Nicene party.
The next emperor (Julian) did not choose sides, but he ruled only for three years.
Valens (364–378) succeeded Julian and revived Constantius’ anti-Nicene policy. He also exiled Nicene bishops to the other ends of the empire and often used force against them. Consequently, when Valens died in the year 378, the imperial capital of the empire (Constantinople), which by then has existed for 50 years, WAS SOLIDLY ARIAN.
Commentators often refer to the First Council of Constantinople, which Theodosius convened in the spring of 381, as the turning point where Arianism was replaced by Nicene Christology, but that council was a mere formality:
Firstly, Theodosius already on 27 February 380, with the Edict of Thessalonica (see Definition of orthodoxy in Theodosius I) decreed that Homoousian Christianity (the Nicene Creed) will be the only legal religion of the Roman Empire and that Christians teaching contrary views will be punished. By means of this edict, Theodosius outlawed all other forms of Christianity.
Secondly, the incumbent bishop of Constantinople was an Arian. Two days after Theodosius arrived in Constantinople, on 24 November 380, and therefore also prior to the First Council of Constantinople in the spring of 381, he exiled the Arian bishop and appointed Gregory of Nazianzus, the leader of the rather small Nicene community in the city, as bishop over the churches of that city.
Thirdly, only supporters of the Nicene Creed were allowed into the Council of 381. The previous Arian bishop and leaders were already banished and Arians arriving to attend the council were denied admission.
The 381 Council, therefore, was simply a formality. Theodosius, with the strong arm of the empire, effectively wiped out Arianism from the Roman Empire.
Edict of Thessalonica
This edict states:
According to the apostolic teaching
and the doctrine of the Gospel, let us believe in the one deity of the Father, the Son and the Holy Spirit, in equal majesty and in a holy Trinity.
We authorize the followers of this law to assume the title of Catholic Christians; but as for the others, since, in our judgment, they are foolish madmen, we decree that they shall be branded with the ignominious name of heretics, and shall not presume to give to their conventicles (places of worship) the name of churches. They will suffer in the first place the chastisement of the divine condemnation and in the second the punishment of our authority which in accordance with the will of Heaven we shall decide to inflict. — Edict of Thessalonica (Documents of the Christian Church, Henry Bettenson, editor, 1967, p. 22)
The term “Catholic” in this quote means ‘universal’. The word “Catholic” only became part of the name of the Catholic Church in 1054, at the East-West schism.
Summarized, Church historian Sozomen reports as follows on the Edict of Thessalonica:
Gratian bestowed the government of Illyria and of the Eastern provinces upon Theodosius. The parents of Theodosius were Christians and were attached to the Nicene doctrines. Theodosius made known by law his intention of leading all his subjects to the reception of that faith which was professed by Damasus, bishop of ROME, and by Peter, bishop of ALEXANDRIA. He enacted that the title of “Catholic Church” should be exclusively confined to those who rendered EQUAL HOMAGE to the Three Persons of the Trinity and that those individuals who entertained opposite opinions should be treated as heretics, regarded with contempt, and delivered over to PUNISHMENT. (Sozomen’s Church History VII.4)
The First Council of Constantinople was a mere formality.
It was customary, in the fourth century, for emperors, as the real heads of the church, to appoint church leaders and convene church councils. Similarly, Theodosius convened the First Council of Constantinople in the spring of 381. It is also known as the Second Ecumenical Council. ‘Ecumenical’ means it represents all Christian Churches and perspectives, but that was certainly not the case in this instance:
Theodosius already outlawed Arianism in the previous year, with the threat of punishment for people that teach anything different.
Gregory of Nazianzus—the leader of the Nicene party in the city—presided over part of the Council and vehemently opposed any compromise with the Homoiousians (those who believed that the Son’s substance is “similar” to the Father’s). (Lewis Ayres – Nicaea and its legacy – Oxford University Press. ISBN978-0-19-875505-0. Retrieved 21 October 2011)
Arians were not admitted into the council. Theodosius already banished the previous Homoiousian bishop and leaders. And 36 Pneumatomachians arrived to attend the council but were denied admission when they refused to accept the Nicene Creed.
Gregory resigned from his office and Nectarius, an unbaptized civil official, was chosen to succeed Gregory as president of the council (Wikipedia, also note 17). Nectarius, as a civil servant, was fully under Theodosius’ control.
The Council, not surprisingly, confirmed Theodosius’ installation of Gregory Nazianzus as Bishop of Constantinople, accepted the Niceno-Constantinopolitan Creed of 381 and dogmatically condemned of all shades of Arianism as heresy.
Contents of the Creed of 381
The Holy Spirit
The 325 Creed merely mentions the Holy Spirit in connection with the Father and Son. It does not refer to the Holy Spirit as theos (“god” or “God”) or that the Spirit is of the same substance as the Father.
The 381 Creed goes much further. The 5 words about the Holy Spirit in the Nicene Creed of 325 became 33 words in the creed of Constantinople, saying:
That the Holy Ghost is “the Lord and Giver of life,”
That He proceeds from the Father and
That He is worshiped together with the Father and the Son.
The 381 Creed, therefore, describes the Holy Spirit much clearer as a separate Person and as God.
The HarperCollins Encyclopedia of Catholicism, “God,” p. 568, states that the teaching of the three Cappadocian Fathers “made it possible for the Council of Constantinople (381) to affirm the divinity of the Holy Spirit, which up to that point had nowhere been clearly stated, not even in Scripture.”
Note: Catholics are not concerned if their doctrines are not found in the Bible because they believe in continued revelation through the church.
The Trinity
As discussed in the article on the Nicene Creed, the present writer does not find the Trinity concept (namely that the Father, Son and Holy Spirit three Persons with three minds in one Being) in the Nicene Creed. It is also absent from the creed of 381. (See the Comparison between the creed of 325 and 381.)
However, the Edict of Thessalonica of 380, quoted above, which was an act of law by the emperor, made Trinitarian theology law. Compare the opening phrases of the Edict of Thessalonica of 380:
“Let us believe in the one deity of the Father, the Son and the Holy Spirit.”
With the opening phrase of the Creed of 381:
“We believe in one God, the Father Almighty …
And in one Lord Jesus Christ …
And in the Holy Ghost”
An edict which Theodosius issued after the Council of 381 is also clearly Trinitarian:
“We now order that all churches are to be handed over to the bishops who profess Father, Son and Holy Spirit of a single majesty, of the same glory, of one splendour” (quoted by Richard Rubenstein, When Jesus Became God, 1999, p. 223).
In other words, the State laws were Trinitarian while the church creeds lagged behind. The first clear Trinitarian church statement is the Athanasian Creed which was not formulated by a Church Council and originated perhaps 100 years later. The contents of Theodosius’s decrees, when compared to the church decrees, support the main thesis of these articles, namely that the decisions, with respect to which Christology the church will adopt, was made by the emperors; not by ecumenical councils.
Post-381 Trinity Development
Mother of God
Relatively soon after Theodosius crushed Arianism, the church formulated the doctrine of Mary as the Mother of God. Britannica reports:
Nestorius, the patriarch of Constantinople, taught that Mary, the mother of Jesus Christ, may not properly be called the mother of God (Greek Theotokos, or “God-bearer”), because she was the mother only of the human Jesus, not of the preexistent Word of God. The Council of Ephesus (431) condemned this teaching.
This matter, and its relationship with the Trinity doctrine, has not been further investigated for this article. According to the 381 Creed, the “Lord Jesus Christ” has been “begotten of the Father.” How Mary may the called mother of God and how this relates to the Trinity doctrine has not been investigated by me.
The Two Natured of Christ
The Arians objected to the creeds of 325 and 381 by asking, if the Son is of the same substance as the Father, why did He say that He does not know the day and hour of His return? Why does only the Father know that (Matt 24:36)? And why did Jesus say that He only do and say what the Father gave Him to do and say (e.g. John 5:30; 8:28). Do such statements not imply that He is subordinate to the Father?
In response to such questions, the church developed the teaching that Christ had two natures:
This council (of Ephesus) gave rise to monophysitism, which taught that Christ only had one nature. It emphasized Christ’s divine nature to such an extent that it effectively negated Christ’s humanity. It compared the relationship between Christ’s humanity and his divinity to a single grain of sugar in the ocean. Pope Leo I (reigned 440–461) led a reaction against this monophysite doctrine that culminated in the Council of Chalcedon (451). This council concluded that Christ had two distinct natures that were neither commingled nor divided and that were equally present in one person. (Britannica)
The key word in the quote from Britannica is perhaps “equally.” The argument is that Christ’s subordination statements in the New Testament must be understood as Him speaking from His human nature.
Most Christians today accept the dual nature theory. Opponents of this theory point out that this does not solve the problem, but makes it worse, for it means that Jesus was not telling the truth when He said that He does not know, for in His divine nature He actually knew.
Chalcedonian Schism
The decisions at Chalcedon led to the Chalcedonian Schism. The patriarchates of Rome, Constantinople, Alexandria, Antioch and Jerusalem accepted the decisions of the council but the Egyptian (Coptic) and Syrian, Ethiopian, and Armenian Christians rejected the Chalcedonian formula:
They declared that Christ’s human and divine natures, while distinct, were equally present through the mystery of the Incarnation in a single person. (Britannica)
In other words, while the Chalcedonian Creed declared that the two natures “were neither commingled,” the opposing party maintained that divinity and humanity were united in one undivided nature in Jesus Christ.
Athanasian Creed
It was the Athanasian Creed—formulated around the year 500, give or take 50 years—which became the standard formulation of the Trinity theory throughout the middle ages. It is still used today by many denominations in liturgy and confessions. This creed was not written by Athanasius. He died more than a century earlier. Neither was this creed produced by any known church council.
The problem with all previous creeds is that they define the Father alone as God, but then proceed to elevate the Son and the Holy Spirit to the same level as the Father. This may mean that we have three Gods (polytheism), while the Bible is strictly monotheistic. The Athanasian Creed, for the first time, strongly and repeatedly emphasizes the oneness of the Father, Son and Holy Spirit in a single Being. It declares that they together are the one God of the Bible. For example:
“So the Father is God;
the Son is God;
and the Holy Ghost is God.
And yet they are not three Gods; but one God.”
As discussed in the article on 
Theodosius I