No, those are both positive true claims. The difference between "God does not exist" and "I do not believe" is that one is a positive truth claim and the other is a position of doubt.
I have a 13 inch penis. Do you believe me? Now, it's entirely possible my penis is that big, but you have no way of knowing if it is. So you respond "I don't believe you" Does this mean you are saying my penis is small? No, it means your rejecting my claim that it 13 inches. Your not contesting my claim with one of your own, your just saying "I doubt that".