Qual è la differenza tra have to e must?

While both of them are quite similar, you have to keep in mind these points:

• MUST is ONLY used in the present tense, so for future and past tense your only choice would be HAVE TO. Examples:

"We must be quiet during the exam."

"When I was a child, I had to live in my grandparent's house."

"In twenty days, I have to take the physics exam."

• HAVE TO is mostly used when we are obeying someone's rules, while MUST is used for more personal duties. Examples:

"I must buy a present for Daniella's birthday."

"To enroll in the course, you have to hold a bachelor's degree."

• HAVE TO is more common in our everyday conversations in comparison to MUST. MUST can be used in a more formal context.
• After modal verbs, such as must, should, and etc, the verb is always in the simple form. On the other hand, when you use HAVE in the third person singular, its form changes to HAS. Examples:

" Lisa must go to the doctor."

"He has to be at work at 8 a.m."

• Another important point you should remember is that when HAVE TO is in negative form, its usage changes, while MUST NOT still have the same meaning. In other words, it is no longer obliging someone to do something, instead, it is suggesting. This example will clarify this point:

"Alberto, you don't have to cook, we can order a pizza" (Alberto can decide whether to cook or not, there is no necessity.)

" You mustn't drink alcohol."

Another good example was given by the British Council which is as follows:

"In a non-smoking area you mustn't smoke, but in a smoking area you don't have to smoke but you can if you want to."