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If you can truly describe it as such, the clearest "denominations" of atheism I've heard defined are "weak atheism" and "strong atheism".
Weak atheism = "I do not believe there is a god" = describes what the person DOES NOT believe but the person has not defined what they DO believe.
Strong atheism = "I believe there is no god" = describes the person's beliefs, arguably making it the more religious of the two.
Of course then you can throw agnosticism into the mix. Agnostic coming from the latin a- meaning "without" and gnosis meaning "knowledge". So by pure literal standards an agnostic would say "I don't know for certain if there is or is not a god", so they acknowledge their ignorance, but do not define their beliefs, putting them on par with "weak" atheists. However, by that definition one could be an agnostic atheist (an atheist who admits they might be wrong) or an agnostic christian (a christian who admits they might also be wrong). But then there are the historical denomination "The Agnostics" whose basic tenet was that the nature of god is unknowable, but in that very definition a belief in some unknowable form of a god is implicitly stated.
Point being, to state that there are "denominations" of atheism is pretty flawed, as atheists are pretty unorganized as religions go, lack any defined heirarchy, dogma, or clear principles. Atheism is an exclusive, not inclusive, term so you you would really just have to ask the individual atheist you are dealing with what they think about any given subject.
But you really probably aren't going to find many atheists tying people to wooden planks and killing them in an attempt to drive demons out of them, so the whole issue is moot.
Just wanted to say, this is a good post. I get tired of having to explain how not all people that don't believe in God are atheists.
I don't know that I'd necessarily use the terms "strong" and "weak" atheism because while the level of conviction may arguably vary, it's a little confusing if not condescending. It might be taken as those people have a weaker bond with their faith (or lack thereof) or that it is somehow inferior... neither of which are necessarily true. In retrospect I don't think there's any need for a categorical "weak atheism" because according to your definition a weak atheist is either someone with no beliefs (agnostic) or someone with a religion which is not atheism.
I think the best way to put it, is that aetheists are people of faith, as are agnostics (depending on which definition you use). The only people that cannot be classified as religious are that other camp of agnostics that truly believe nothing, some of which (like myself) are grounded in science. (If you have no beliefs, you still must act as if you do, so agnostics with no beliefs have to form pseudo-belief systems to act upon. I use the scientific method and inferential and deductive logic myself. Others use things similar to witchcraft or even other religions.)
Personally I find faith unsensible. People readily admit that faith is not knowledge, because if you knew, it wouldn't be faith. Well, if you don't know, then why pretend like you do? Why not just accept that you don't know? Is it so hard to be honest with yourself about your limitations? Seems much harder to me to try to convince myself of something which I have every right and reason to doubt.
