Distinct in the sense of being orthogonal. It is possible to believe there is no god while admitting that you do not know that there is no god. Knowledge is the intersection of truth and belief, and since the truth value of the god hypothesis can never be conclusively determined, the most we can ever achieve is a strong suspicion. Atheists, by and large, are agnostics. But people who call themselves agnostics are different from atheists, in my experience, in their willingness to entertain the possibility rather than reject it. I agree with the earlier poster who thought this was an odd notion, because there is an uncountably infinite number of unfalsifiable propositions to entertain. What makes the god hypothesis worthy of this special consideration, when we casually reject all the others?
Incidentally, dictionary.com defines disbelief as "the inability or refusal to believe or to accept something as true" which strikes me more as not believing there is a god than believing there is no god. So, by your definition, you're an atheist if you believe there is no god OR if you merely refuse to believe there is one.