Earlier quoted context omitted.
So do Mormons and Jehovah's Witnesses. How do you distinguish between "having a different God" and "having different beliefs about the same God"?
Depends if you believe it's the same god or not... But if we both claim to know a guy called John Brown, but I say he's kind, generous, hard working but a little dim and you say John Brown is hedonistic, self-entered and brilliant, are we talking about the same person? Normally if our descriptions are similar enough that we can chalk it up to perspective, we might think it is. But if our descriptions of the person be…
So like you say, if the overlap between your A,B,C,D and my A,B,C,D is sufficiently small we should probably acknowledge that it's not the same entity. See also: Ship of Theseus.