As said above, they mean the same thing. For me at least, must is used more formally or for emphasis. The phrases you've used below are quite casual, so I don't think you'd use 'must' for any of them. You normally find 'must' in instructions or other formal situations; for example, on the front page of your exam paper: You must use black or blue pen. For emphasis, I would sometimes say something like: I MUST get to the shops today to return that shirt. Below I've said what I would use for your phrases: I have to go now, my train leaves at 17pm. - I would use 'have to' or 'need to' I must read this book for next week. - I need to... I should study for the exam, but I'm not feeling good. - I should.. or if you're trying to study but not doing very well, then I would say 'need to' You have to buy something to eat on the way home. - You should.. or (I don't have anything for your dinner,) You'll have to.. I have to wash all these dishes, but now I'm going to watch some Tv. - I have to... I have to take out the dog. - I have to... You must come back in 5 minutes, or I'll go without you. "You have to..." Hope that helps!

No they don't mean the same. "Have to" means you have a duty, obligation to do something. "Must". You will do it no matter you like it or not.

"Have to" and "must" can be used the same, but "have to" sounds more informal than "must".

There is no difference