Merely a semantic difference. Whether you say that you do believe that gods don't exist or you don't believe that gods do exist you are saying the exact same thing.

An atheist believes that atheism is true. An atheist believes that theism and agnosticism is false. An atheist believes that it is the case that no gods exist.

This type of statement fascinates me. Not because it has any philosophical significance (it can be quickly pushed aside) but because it has personal significance. It's an attempt to blur the atheist's stance in order to make his position harder to attack. If he somehow doesn't believe in anything then you are unable to say what he believes is false.

Conveniently, however, atheists like to use this little thing called logic (or so they say, just like most people), and in accordance with logic when we symbolize the two sentences we find that they are analytically equivalent.

If we take "X" to mean "god exists", and we wanted to say either "it is the case god doesn't exist" or "it isn't the case that god does exist" we would style symbolize the sentence as ~X. This is knowledge taught in Philosophy 101 (I'm not saying this as an insult, but literally, this is one of the first things a philosopher learns).

This type of argument is really a great big straw man for any atheist arguing his position. All beliefs aside, the atmosphere of the God debate has become increasingly philosophically bankrupt on both sides, petty semantics such as this being the example.