I would suggest that the right framing here is in terms of multiple dimensions of modal logic.
I can assert that the dog in front of me is brown. I can be certain or uncertain of his brownness. But if it were controverted, even if I were quite certain, it would not affect me deeply. I hold this belief largely in an alethic mode, as knowledge. All that matters about it is its degree of certainty.
I can also assert that he has a personality. I can again be certain or uncertain, but the answer holds more meaning. I talk to him. He knows that when I say 'OK', he has effectively made a request, and we are pursuing his agenda. But that is hardly proof. I am not altogether certain. Yet when that is controverted, it hurts -- I feel foolish. I do many things on the basis of his limited personhood that I would not otherwise do. I hold this belief in a doxastic mode, as an everyday belief. What matters primarily is the degree to which it informs my actions.
Finally, I can assert that hurting him is to be avoided. Again this can have both of the other dimensions, I can be uncertain, and I may or may not consider this when acting. But when I don't, it hurts in a different way -- I feel less valuable as a person. I hold this belief in a deontic mode, as a moral belief. What matters primarily is the degree to which I bear it as a duty.
To me, it seems that the assertion "There is no God" can clearly be held in each of these ways. The average person might actually hold it as an alethic assertion, like Montaigne, it might have no effect on their life, if it is their tradition, they go to Church anyway. The agnostic probably holds it as a doxastic assertion. They refuse to act as though there is a God, because it seems silly. I only consider those atheists who hold it as a deontic assertion, who feel driven for reasons of internal consistency to assert it with force.
Something is a belief, for me, only if it can have all three of these dimensions. Mathematical and scientific facts are not beliefs, because they are held strictly as knowledge. You act on them, but you do not choose to. Random observations that have no effect are not beliefs because they lack influence over action. Totally abstract points of logic are not beliefs because they might guide your deductions, but they do not influence your real judgment of right and wrong.
I believe my dog is brown, but it is not in this sense a belief. That he has a personality entails the fact that hurting him is wrong, so it becomes a belief.