Difference between must and have to?

They mean the same thing, it's just a case of having two different ways to say the same thing.

These are both ways of expressing obligation. With "must" the obligation comes from the speaker, "You must wash your hair, it's filthy" or "I must take a shower, I stink!" With "have to" the obligation comes from somewhere else or for routines, "I have to wear uniform for school." "I have to read in bed each night or I can't get to sleep"