Erebus
Well-Known Member
I think beleiving in gods but not worshipping them would be a form of deism, wouldn't it?
That's certainly one possibility. Such a stance could also be the result of misotheism, dystheism and other negative views of gods. A henotheist could arguably fit here too in that they allow for the existence/possibility of other gods besides the one they worship.
To the OP, I have to admit I've pretty much only heard non-theism being used as a synonym for atheism. On occasion I've seen it used to distinguish somebody from the more "new atheist" types, but that's about it.