Generally, at least in the UK, must and have to are used interchangeably in the present tense. You must drive on the left and have to drive on the left are understood to have the same meaning of obligation. I would say that must suggests that the DVLA (UK driving authority), for example, is making a statement you have to follow. They say that you must do it. Whereas have to implies that it's just a rule that needs to be followed, it's unclear who has made the decision but it must be followed. For example, - "The highway code says you must drive on the left in the UK". - "Don't you know that you have to drive on the left in the UK"?

The distinction is not that strong. Practical English in Use 3rd ed. by Swan covers this in sections 361 and 362. Briefly, Americans use them interchangeably, and increasing the British are doing so too.

Although that rule is a great way to remember how to use "must", specially when reading british literature you'll find that they prefer to say "must" instead of "have to". It really just comes as a preference since, in the anglo-saxon mind, they kind of mean the same thing. One thing I've noticed is that in US literature and day to day life, they use "must" as a way to make an emphasis on the obligatory nature of the action. Just like a parent would say to their child "you must finish your homework before playing videogames".

I agree with you. In spoken English, however, "must" and "have to" are commonly used interchangeably. In the US you can hear all the times things like "you have to watch that movie! " You can see a similar phenomenon with the verbs can/may. Everyone nowadays asks "can I go to the toilet? " when what they mean is "may I go to the toilet? ".