Same thing. Different nuance. Faith is a very strong word. It means to believe in things you can not see.

Both terms mean the same but there is a subtle difference. Believe is generally based on facts that you are confident about something and you are believing it. In this case you are confident about the other person. Faith is usually used to determine to achieve extraordinary goals. "Like Wright brothers had faith in their machine that it could fly". - The machine never flew but they had a small hope. Usually its blind - "blind faith". Similarly "I have faith in you" is more stronger sense of feeling. It implies that my inner feelings say so.