Was the "Nicene Creed" of AD 381 an update of the Nicene Creed of AD 325? 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?
There are many differences in wording, although with very similar meaning, allowing the assumption that the two creeds are independent of each other, linked only by being based on an earlier baptismal creed. Even so, the authors of the 381 Creed were inevitably aware of the Nicene Creed of 325. Actual evidence that the Creed of 381 is dependent on the Creed of 325 is found in the words "being of one substance [being] with the Father."

Elaine Pagels says, in Beyond Belief, page 174, that this phrase was inserted into the Nicene Creed at the insistence of Alexander, bishop of Alexandria, in order to fully exclude the views of Arius, whom Alexander had excommunicated for alleged heresy. Thus, these words could not have been received from a pre-Nicene document, and their existence in the Creed of 381 makes that document at least partly dependent on the Nicene Creed of 325. 

Further circumstantial evidence is that the longer and more sophisticated wording of the later Creed is a theological elaboration that is typically found in later versions of a document, and therefore potential evidence that the 381 version is an update of the 325 document rather than of an even simpler, earlier document. The reference to Mary likely to be a result of the Mariology that developed over the later decades of the fourth century.