There is a big difference between having a belief and not having a belief. If you believe there is no god, you are asserting there is no god - that this is a conclusion you reached, to your satisfaction, after examing some body of evince or invalidated or unsubstantiated claims. If you do not have a belief about the existence of any god, then you have no belief - you have not come to any conclusion. And that is all it means - it does not imply you think there could possibly be one, it just means you don't have enough information to lead you to believe that there is one. Either way, you're an atheist (i.e. not a theist). The other option is that you believe there is a god (usually a specific one), which would make you a theist.
When someone says they don't believe in a god, you might ask them whether they mean they have no belief, or if they believe there is no god, but generally it usually means they're reasonably sure there is no god.
The final option, apathiesm, is more concerned with othe matters to invest the time or energy to entertain such pointless questions about whether or not a god exists, and where's my sandwich?
