This is hard to put into words that have not already been said… and well, just plain hard to put into words.
I’d have to say that I initially thought they meant pretty much the same thing. Now, I see they do not, and that one builds on the other and you need Both to get closer to the goal, Jesus. So:
The simple act of just acknowledging Jesus’ presence is crawling, or even just knowing the name of God, the name of His Son and knowing somewhere in your depths that it means something more than just a name or even a swear word.
Faith is the action, the movement of belief.
Belief is like learning how to stand before learning how to walk. You must strengthen your leg muscles through the movement of standing and with regular practice, otherwise walking will be impossible.
Faith is the walking. You have the muscles built through standing (and crawling), and now you are applying it in a very literal way through moving forward (and/or backwards). But, you are trusting in those early developments (being sure of what you hope for and certain of what you do not see. Hebrews 11:1), trusting that they will hold out as you are walking because if they don’t, you will not keep moving forward or even standing.
So, in the development of faith, one must first believe. Then in order to continue to grow, one must follow the example of another and, in the both the case of Belief and the case of Faith, that example would be Jesus because He is the only one who can do what God does; Jesus does as the Father does, and we do as Jesus does (John 5:19-23). If not, you’ll just be standing still in one place; or, you may even revert all the way back to crawling, and you’ll miss so much when you’re so very low to the ground.