This is a big question. One could write a book on the topic! (wait, the Chazon Ish actually did, and so did R Avigdor Miller).
But in a simple way (taken from Ben Tzion Shafier here) emunah is the knowledge that Hashem created and continues to run all of Creation and that he is involved in the minutiae of my daily life.
Bitachon is acting on that knowledge and relying on/trusting Hashem. It is a sense of depending on Him to watch over and protect me.
Emunah is a state of understanding. Bitachon is a state of trust. Emunah comes from studying this world and seeing that there is a Creator. Bitachon is the state of trust that comes from recognizing that that Creator is good, kindly and wise—and that He cares deeply for His creations.
See also R Hershel Schachter here
Bitachon requires that we act in accordance with our emunah, i.e. in
accordance with this principle of faith that there is hasgacha pratis.
While one must engage in hishtadlus, he should not fall to pieces
considering the possibility that he may accidentally (i.e. not in
accordance with the divine will) die, etc. The outcome of all
situations is dictated by the will of Hashem, and everything Hashem
does is ultimately l'tov.