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.“
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.
For more information, see Arian controversy – Wikipedia.
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.”
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.