A key distinction between ‘must’ and ‘have to’ can be found in the negative forms. Whereas ‘You must go’ and ‘You have to go’ can be regarded as broadly the same in terms of meaning, ‘You mustn’t go’ and ‘You don’t have to go’ are quite different, the first indicating that going is prohibited in some way, or even dangerous, while the second implies an absence of obligation or need.
Another difference between ‘must’ and ‘have to’ in the sense of obligation can be found in the nature of the obligation. It is possible to say ‘I’m sorry. I can’t come to the meeting tomorrow because I have to go to the dentist at 3 o’clock’ but not ‘I can’t come to the meeting tomorrow because I must go the dentist at 3 o’clock’. On the other hand, if you have a raging toothache, you would probably say ‘I really must go to the dentist’, although ‘have to’ could replace ‘must’ in this sentence. A generalized distinction would be that ‘must’ refers to an internal need or obligation while ‘have to’ is used to refer to an external need or obligation. It is probably true to say, however, that ‘must’ can generally be replaced by ‘have to’ but ‘have to’ often cannot be replaced by ‘must’ so in terms of teaching, it is probably a good idea to teach ‘have to’ for obligation because it is nearly always correct whereas ‘must’ is often inappropriate. ‘Must’ and ‘must not’ are useful for official notices and instructions, e.g. ‘You must carry your passport at all times’ and ‘You must not smoke in the toilets’.