We use have to (do something) to say that it is necessary to do it.
eg. She can’t come with us tonight. She has to learn for her exam.
Must is similar to have to.
We use must to give own own opinion, to recommend somebody to do something but have to is also possible.
eg. (1) I haven’t seen my family for three years. I must call them. (it is necessary)
eg. (2) This is a really good movie. You must see it. (I recommend this)
We use have to to say that somebody is obliged to do something.
eg. Sue has to work at the weekends.
We use must in written rules and instructions.
eg. You must wash your hands before breakfast.
When talking about the past we only use have to.
eg. She had to go to bed early.
When used in negative form, mustn’t and don’t have to have completely different meanings.
eg. (1) Mark was fired this morning. Until it’s official, you mustn’t tell anyone. (= don’t tell anyone)
eg. (2) You don’t have to tell her about what happened at work. (you don’t need to do it but you can if you want)