We normally use must when the authority comes from the speaker.

We normally use have to when the authority comes from outside the speaker.

Mother: You must be home by 10 o'clock. (I insist.)

Daughter: I have to be home by 10 o'clock. (My parents insist.)

I've got a terrible pain in my back. I must go and see the doctor. (I think it is necessary.)

I have to go and see the doctor at 9.00 tomorrow morning. (I have got an appointment.)             

You must drive carefully. (I insist.)                                                  

You have to drive on the left in Britain. (That is the law.)