Believing is something much simpler than trust. When I believe a person I can believe a fact that he or she said at the time, even though I might not necessarily trust the person. I believe a fact but I do not necessarily trust the person. Of course the meanings of these two words are usually mixed up on our daily lives, but they are completely different words. Trust is much stronger, when you believe the person and completely think that person is honest etc etc, than it becomes trust. You can believe in any isolated fact or thing, but you usually don't trust as many people. You can also check dictionaries such as merriam webster and oxford for a complete book like definition if you still have doubts. Hope I helped.