'Must' and 'have to' mean basically the same thing when used in a positive sense. They are slightly different in tone. 'Must' is used when we are forced to do an act when something important happens. "I must leave - it's an emergency." "Have to" is used for more daily items. "I have to start dinner now." In actual practice, we use 'have to' in place of 'must'. It is not an important difference. The big difference is in the negative. "You must not do A" = You are not supposed or allowed to do A "You do not have to do A" = You can do A, but it is not required. A large difference, you'll agree. One more important fact. 'Must' does not have a form in the past tense. Instead, you would say 'did not have to'. "He did not have to go to school because he was sick." = It was not necessary for him to go to school.

We can also use 'have to' to express a strong obligation. When we use 'have to' this usually means that some external circumstance makes the obligation necessary. * I have to arrive at work at 9 sharp. My boss is very strict. * We have to give him our answer today or lose out on the contract.

Чаще всего - в случаях, когда кто-то что-то должен сделать, или ему приходится. В остальном - это синоним must. То есть must более "жесткий", что ли. Кроме того, have to может использоваться в любых формах, в том числе - в прошедшем времени. Также, отрицание с глаголами имеет разный смысл: must not - запрещено, don't have to - нет необходимости