Emunah is Hashem is, was and always will be. He created the world, and everything in it.
Bitachon is trusting that Hashem will take care of you in any situation.
Believing that what happens is for the best is a positive middah and a high madreiga, but I’m not sure if which category it fits in exactly. Certainly, what Joseph said is an example of bitachon – trusting that Hashem will give you the emotional and financial means to handle the number of children that He gives you.