This and similar charts explain it pretty well.



Basically, a/gnostic determines whether you claim to have proof/knowledge, while a/theist determines whether you claim a belief. I don't believe God (or a God) exists, but I don't claim to have proof/knowledge of that, therefore agnostic atheist.

The types that argue that God does not exist as if that statement is somehow factual would be considered gnostic atheists. Desmethones seemed to be approximately that in the past IIRC, though I could be recalling incorrectly and I wouldn't be surprised if his views have shifted over time (as mine have.)