They are interchangeable. As far as subtle differences go, 'must' is probably more dramatic and carries greater urgency (but only very slightly so) while 'have to' is probably used more in everyday speech. You should feel comfortable using either.

Firstly, "must" is an auxiliary verb. It is to be obliged or bound to by an imperative requirement. In other words, it is to be under the necessity to or need to. Secondly, "have to" is also to be obliged; therefore, a must. From your examples, you're right!you can use either one of those word/phrase!:) ----hope that helps.

There are some subtle differences, but IN GENERAL we use "must" when the pressure comes from ourselves, and "have to" when it comes from others. Examples: "I must stop smoking." (I am telling this to myself) "His doctor told him he had to stop smoking" (another person said it) "Must" is also used in warnings ("You must be careful in train stations--there are a lot of pickpockets") or in rules ("All swimmers must shower before entering the pool").