Must expresses the speaker's feelings, whereas
have to expresses, above all, an impersonal idea:
You must come. You are obliged to come (I require that you come)
You have to come. You are obliged to come. (There's a rule requiring you to come)
Must I wear this tie? Am I obliged to wear this tie? (What do you think?)
Do I have to wear this tie? Am I obliged to wear this tie? (Is there a rule about ties?)