Not sure if anybody has said this previously, but my option isn't listed: I don't believe that there is a god, rather than believing a god doesn't actually exist. Is that different aside from semantics? I think so.
If by "I don't believe that there is a god" you mean the same as "I have no belief in a god' then the option is covered by "Atheist type A – I neither believe nor disbelieve a god actually exists". It's not covered by "Atheist type B – I believe a god doesn't actually exist".
However, "I don't believe that there is a god" could be read to mean either "I believe that there is no god" or "I know that there is no god".