I was taught that emunah means believing that something can/will happen. To M’s example above, emunah would mean that someone who wants to sit and learn would trust that Hashem will provide for his needs.
Bitachon is belief that whatever Hashem does is for the best. So in the same example, if the person is sitting and learning, without going to earn a living at all, and he ends up getting evicted from his home, bitachon would be believing that this was the best thing that could have happened to him.