There is no difference. I have to go to school. I must go to school. They both show a requirement or compulsion. It's important to note that the negatives are completely different. I don't have to go to school. <-- this is no need or requirement I must not go to school <-- requirement that I DON'T GO

If you're facing a test, then this is the rule you need to remember: "Have to" is used when the obligation comes from outside. You have to work 45h a week because the boss tells you to. "Must" is used when the obligation comes from within. You must work work 45h a week in order to earn enough money to live by. Exams will test you based on this difference. That said, "must" can often stand as a strong equivalent of "have to" (ie. making the obligation a personal matter). And as Mojave pointed out, using them in the negative form is a different matter. Modals are tricky things. There's so much more to learn about them.

We use MUST when we say something that is essential or necessary. e.g. You must visit us soon. Must is a modal auxiliary verb. It is followed by a main verb. The structure is subject + must + main verb MUST expresses personal obligation. It expresses what the speaker thinks is necessary. Must is subjective. e.g. I must go home. HAVE TO is when we say that something is obligatory, e.g. children have to go to school. Have to is often grouped with modal auxiliary verbs for convenience, but in fact it is not a modal verb. It is not even an auxiliary verb. In the structure, "have" is a main verb. The structure is subject + auxiliary verb + have + infinitive (with to) e.g. I have to go to work. Have to expresses impersonal obligation. The subject of have to is obliged or forced to act by a separate, external power (for example, the Law or school rules). Have to is objective.