Faith believes in what is true. Faith is being convinced of the truth, being certain of reality, having evidence of things you can not see, and faith is believing, hoping in, embracing, grabbing a hold the truth.
Heb 11:1 (NIV) Now faith is being sure of what we hope for and certain of what we do not see.
Just knowing the truth is only half of faith. Faith requires being convinced that what we believe in is true, God's word must be hoped for, embraced, seized!
Believing is not exactly the same as faith. For belief to be faith, it must believe on what is true. Yet Scripture gives examples of situations where belief alone is required, even commanded. Like, there's no time for evidence collection, to wait, to hear, for certainty. Just believe. Like Peter walking on the water—he had no time to think about getting out of the boat or not…don't think, act! God even requires us to believe in him when, temporarily, the evidence looks bad: to trust. God requires belief and trust in moments of human weakness, but faith is what makes us strong. Faith is the state of being convinced about what we hope for.
So since faith is what makes us stronger in our walk with God. I would say that Faith is stronger then belief.
When it comes to mountain moving I believe the word “mountain” represents things that I need God to answer. Not physical mountains. Could God move one for me, yes he can but I still hold on to it being something that I take to God in prayer, such as, maybe I’m in trouble with my finances, not working and things seem to be as BIG as a mountain. So I pray and believe and have faith that God is going to work those details out (removing the mountain). I didn’t mean to write a book, sorry :-)