In the positive they're very close. Must often shows the speaker's own feeling or a written rule: I must call my mum. Passengers must wear seatbelts. Have to shows an obligation from outside: I have to wear a uniform at work. In the past, only had to works.
Same situation, two choices. Pick an example.
I must call my mum. It's her birthday.
The speaker feels it's necessary, or it's an official written rule.
I have to call the bank before 5.
Someone or something else makes it necessary: your job, the law, the situation.
| Rule | Must | Have to |
|---|---|---|
| Who decides | The speaker, or a written rule | Someone or something else |
| Past | No past form | had to |
| Future | No future form | will have to |
| Questions | Must I…? (formal, rare) | Do I have to…? (normal) |
| Negative | mustn't = not allowed | don't have to = not necessary |
Yesterday I _____ wait two hours for the bus.
Paste an email or an essay. Clarigram marks the mistakes you actually make, shows the rule behind each one as a picture, and builds your practice from them.
Yes, especially in British English and in speech: I've got to go. It's less common in questions and in the past.