Sometimes we can use must or have to to mean the same thing.
Example:
I need to be at the airport in one hour, so I must / have to go.
Generally, we use must for expressing personal feelings, and have to for expressing facts.
Example:
That new restaurant is great! You must go there!
You have to turn off your mobile phone in a museum.
We use must for the present or future, but not the past. We can use have to for all tenses (i.e., change have to to had to).
For negative statements and questions, we generally use do / does / did with have to.
Example:
You don't have to participate in the phone conference. CORRECT
You have not to participate in the phone conference. INCORRECT
Why did you have to tell the boss what I said? CORRECT
Why had you to tell the boss what I said? INCORRECT
Must not / mustn't and don't have to have different meanings. Must not / mustn't means it is forbidden. Don't have to means it is not necessary.
Example:
You mustn't do personal work on the company's computers.
You don't have to attend the meeting if you don't want to.