Pretty much the same. The difference is minor: have to = suggests that something external is the cause; e.g. The boss says I have to go. must = suggests internal urgency; e.g. I must go or I'll be late.

"Have to" and "must" have the same meaning in the affirmative and interrogative forms when referring to obligation. Some people think that "must" is slightly stronger, but for all practical purposes, they mean the same thing: Doctors have to attend medical school for several years before they can practice medicine. Doctors must attend medical school for several years before they can practice medicine.