Actually... no. Belief is something you think to be true. It can be something very profound or rather simple.
The belief that the animals had left the shelter led the hunters to go after them. (Nobody would use "faith" in this case).
Faith is itself a belief, but a lot more profound. You may have faith in God, or in your family.
The expression "my faith" would refer to "my religion". But the expression "my belief" can refer to an specific dogma taught by my religion, or it can also refer to something you believe that has nothing to do with religion.