Theism is faith-based doctrine, atheism is rejection of theism
- Faith: belief without evidence to validate the belief
- God: a person with a will, that and that will cannot be disputed by humans
Theism is not just the belief that a god of some kind exists, because that is deism. Theism goes further than deism, as described by Christopher Hitchens:
[You] may not wish to abandon the idea that there must be some sort of first or proximate cause or prime mover of the known and observable world and universe.
But even if you can get yourself to that position […] all your work is still ahead of you. To go from being a deist to a theist — in other words to someone who says: God cares about you; knows who you are; minds what you do; answers your prayers; cares which bits of your penis or clitoris you saw away or have sawn away for you; minds who you go to bed with and in what way; minds what holy days you observe; minds what you eat; minds what positions you use for pleasure — all your work is still ahead of you, and lots of luck. Because there is nobody, there's nobody, even Aquinas had to give it up, there's no one who can move from the first position to the second
So in short:
Theism is faith-based (the-) doctrine (-ism).
Atheism is therefore rejection of faith-based doctrine. In a nutshell, this is how the conversation goes:
Theist: I know what the higher, divine will is, and you would do best to follow it
Atheist: No, I do not think so. I reject that notion of yours.
So the qualities of the god does not actually matter. The god in question may be the Abrahamic god, any of the Hindu gods, or even a human god like Emperor Hirohito. What matters is the following:
- The believers claim that the god-person's will is known, at least to them
- The believers claim that the god-person's will is indisputable
Atheism is simply to disagree with the latter or both of the points above. Therefore: no, it is not true to say that atheism is the same as theism.
And to finally answer your question: the only common qualities that gods of various religionms has is that
- They are a person/persons
- They have a will/a plan
- That will is indisputable by humans