We are talking about two different things: belief and knowledge. Atheism is a statement about one’s belief. A theist believes in a god. An atheist does not. An atheist has weighed the evidence and found the atheist case more compelling than that of the theist. In legal terms, the atheist finds it more probable than not that gods do not exist, while a theist takes the opposite position. There are really only two positions possible here.
Agnosticism is a statement about knowledge. In fact, knowledge is the root of the word. It describes someone who does not know whether there is a god or not and most people attach to the knowledge the requirement of complete certainty. This is not a very useful descriptor since if you think about it, no one really knows whether a god exists, because the existence of gods, which are by their nature beyond time and space and not subject to our physical laws, is not provable or disprovable to that level of certainty. So all atheists are really agnostic atheists and all theists are really agnostic theists, even if they don’t admit to it.
The term agnostic became popular, I believe, as a result of the stigma associated with “atheist.” It was a way of throwing one’s hands up in the air and saying “I just don’t know, so I’m not going to take a side,” allowing one to live as an atheist without calling oneself an atheist, no doubt for practical reasons. But knowing and believing are different things. We all decide not to believe in things even though we can’t affirmatively disprove them. So any distinction between atheist and agnostic on these grounds is really of no value.
It does make sense to think about strong atheists and weak atheists, though. The strength of one’s atheism would appear to be based upon how far the person believes the scales of evidence are tipped against the existence of gods (or, when addressing a particular religion, the specific god associated with that religion). The weakest possible atheist would be the one who sees the scales as balanced, with the evidence exactly equal on both sides, but concludes that theists have the burden of proof to tip the scales, and thus comes down on the side of atheism. But if they conclude from this process that there is no god, and live their lives accordingly, then they are atheists.