1. Must expresses the speaker's feelings, whereas have to expresses, above all, an impersonal idea:

Ex :
A. You must come. (I require that you come)
B. You have to come.(There's a rule requiring you to come)

C. Must I wear this tie? ( What do you think?)
D. Do I have to wear this tie? (Is there a rule about ties?)

2. Have to mainly expresses general obligations, while must is used for specific obligations:

Ex :
A. I have to brush my teeth twice a day.
B. I must tell you something.