How can you tell if two religions are in fact different religions or variations (or sects) of the same religion?

I submit that a good question for this one is "How well can members of the two religions argue?" This is similar to a test for "Are two languages really just forms of the same language?" where the test is can people speaking the two languages understand each other? Someone speaking "Bostonian" and someone speaking "San Franciscan" can understand each other, so we say they both are speaking English. Someone speaking Japanese and someone speaking French cannot understand each other, so we say Japanese and French are two different languages.

(And then there are ones where this test is of limited use - e.g. Spanish and Portuguese or Mexico City Spanish and Chilean small town Spanish.)

Similarly, Presbyterians and Baptists can argue. A Presbyterian will say "The Bible says such and such" and the Baptist will have to respond with something like "You are not applying the Bible correctly, what that passage means is this and that.” So Presbyterians and Baptists follow two forms of the same religion.
But, if a Presbyterian says "The Bible says such and such" to a Muslim, the Muslim will respond with something like "So what, the Bible is not a reliable." Then when the Muslim says "The Koran says this and such" the Presbyterian can respond with "So what, the Koran is not authoritative". Presbyterians and Muslims follow two different religions.

Again there are some cases where this question is less useful. Presbyterians and Roman Catholics for example. On the one hand both can and will quote the Bible to each other, and neither can say "So what". But Roman Catholics also have Papal Authority and Tradition to which the Presbyterian can say "So what". I do not know enough to know how that works out since I am not sure exactly how Papal Authority and Tradition work in Roman Catholicism.

On the other hand, it does appear that Mormonism is a different religion than either Presbyterianism or Roman Catholicism. The Book of Mormon (and the teachings from Joseph Smith and others) seems to be too important to Mormons. This does not necessarily mean Mormons are bad or that Mormonism is false, just that neither Presbyterianism nor Roman Catholicism are the same religion as Mormonism.