Is there a difference? I think so.
I am presenting a leadership study from the life of Moses. At this point he is 80, and has been living as a shepherd for 40 years. When he was 40, he thought he was the answer to his oppressed people's problems; Acts 7:25 For he supposed his brethren would have understood how that God by his hand would deliver them: but they understood not.
He wasn't ready, they were not ready, and God was not ready to use him. SO, he failed - morally failed and became a murderer.
Now God calls him but he has had 40 years to consider himself a failure. After a powerful presentation by God about what He wants Moses to do and a great outline of how it will be done, Moses says, (I paraphrase) "Send somebody else".
He believes in God. He knows his people need to be delivered. He does not believe he is "da man" any more.
My point: there is a difference between unbelief and doubt. Unbelief rejects, doubt questions. God deals is Grace with doubters. God transforms doubters to people who change the course of world history - like Moses.