If you must do something it is more important than when you have to do something. If you must go to the doctors, it is more important to go then when you have to go, there is more emphasis to 'must'.

In common use, they are equivalent. However, must only has a present tense, whereas have to has past, present, and future tenses. Yesterday, I had to go to the doctor's office. Today, I have to go to the doctor's office. (= Today, I must go to the doctor's office.) Tomorrow, I will have to go to the doctor's office. There is one tricky case where they are not equivalent. I have to do X (equals) I have no choice, I must do X I don't have to do X (equals) I have a choice to do X or not I must not do X (equals) I have no choice, I must avoid doing X

thank u,kate