There is a significant difference.
Must is personal obligation, have to, an external obligation.
"You have to serve in the army in some countries"
"I must do more exercise"
The second is a personal goal, the first is a externally imposed obligation.
Sometime the two categories coincide, however.
"You must/have to renew your passport if you want to go abroad"
But the emphasis is different- "must" stresses the personal (you need a new passport because you want to go abroad to visit your friends, perhaps) while "have to" emphasises the external obligation (the fact that you need to get the new passpost because its a legal requirement for foreign travel).