Seems what's being said here on the one side is that a 'cult' is a sub-section of a 'religion' - no matter that the cult represents a small or large percentage of the total worshipers. Generally I define religion as 'res ligio' = 'connecting all things'. On that basis one cannot discount an interpretation of the word cult as necessarily diminutive in terms of the whole.
And on the other that the word 'cult is another word for an entire religion.
So a subsection or offshoot (however large of small) of a huge religion can be a cult as seen by others in that religion, but a vast religion could not be described as a cult by outsiders except in a perjorative and likely innacurate sense.
It somehow seems the Cult of Talos is an offshoot of the Imperial Cult, which is in itself at the same time (Dragonbreaks allowing) or at a certain point was then subsumed into the Cult of Talos (swallows its own tail) and that both are offshoots of or additions to the Nine Divines - or someone does not like the Imperials (likely the mer that) and has found a way to diminish the Imperial religion in the eyes of its own prospective members. I suppose there are mer on the Elder Council?
All in all the facts as given generally seem to twist according to the perspective of the original and subsequent writers - something we are all aware of, but that many often have trouble delivering clearly in their own posts and threads on this forum because we seldom roleplay our responses.
Strangely enough a very large number of the Loreful texts in-game, that are actually written by a third party and based on received information are spread around as absolute truth in this Forum, even when the text itself warns the reader that it is not first-hand.
Anyways, hopefully I can leave you to enjoy your word-game in peace now