When people talk about "The Nicene Creed," it seems that they are often referring to the document associated with the Council of Constantinople (AD 381). I'm sure there are many reasons for this, one of which being the similarity between that creed and the one produced by the AD 325 Council of Nicaea (cf. Wikipedia's comparison of the 325 and 381 creeds).
However, I've learned that it is not universally held that the 381 council actually meant to update the 325 creed. Britannica says:
Additional discoveries of documents in the 20th century, however, indicated that the situation was more complex, and the actual development of the Niceno-Constantinopolitan Creed has been the subject of scholarly dispute. [...] It was probably based on a baptismal creed already in existence, but it was an independent document and not an enlargement of the Creed of Nicaea.
If this is the case, then it would seem to be incorrect to refer to the AD 381 creed as the "Nicene" creed, or even the "Niceno-Constantinopolitan" creed (as Britannica does), since there would be no direct connection between the two creeds.
What is an overview of the historical evidence regarding the origin of the AD 381 "Nicene Creed"? Did its authors intend for it to be an update of the AD 325 creed? Did any contemporaries call the AD 381 creed "Nicene"?
Or is the 381 creed better understood to be an independent creed?