Hi! I've written a piece on English modal verbs in the 21st century, but it's too big to post here. The bottom line is that I've been teaching ESL in the Russian Federation for more than six years, and can't begin to understand why Russians are taught that there is really a difference between "must" and "have to." And it just floors me when I see people say "mustn't" and needn't." It's like, hello, are you Charles Dickens or what? I teach my students that there is NO difference between "have to" and "must." Besides being a native English speaker for more than 50 years,I know NO native English speakers who differentiate, and in the negative we say I don't have to or I don't need to. And the Oxford ESL publishing mafia continues to inculcate these crazy modal rules, but not all.
I don't differentiate between "must" and "have to" either.
Like Bhaisahab, I also use "mustn't" and "needn't" where appropriate.
***Neither a teacher nor a native speaker.***
Mustn't and needn't are only common in British English.
There is a difference between must and have to.
Must is your own choice, but it is important for you.
I must stop laughing about everything.
There is no law or anything that forces you not to laugh, but if you continue to laugh constantly, others might think you're crazy.
I have to stop to smoke in the library.
If you don't stop it, they will throw you out.
I must visit my friend.
You were not told/forced to do that, but you decided it would be the best because you haven't seen him/her for months.
If you don't visit him now, you will have to wait further months, so you must do it now.
I have to go to the police station.
You received an invitation (witness statement).
If you don't go, you'll break the law.
Must not and don't need to:
I must not think loudly.
I always give away my secrets because I cannot be silent.
It's bad for me.
I don't need to play every day.
There are also many other possibilities, like going out, meeting friends, etc.
It's not necessary that I play every day, especially during the summer.
I could play every day, but I don't want to, because I don't need to.
If my examples aren't good, I will think about something new...
I don't think you mustn't and you don't have to are the same. You can get by without worrying about the differences in the affirmative, perceived or real.
I must go to the bank = I have to go to the bank.
I mustn't go to the bank = It's important that I don't go to the bank.
I don't have to go to the bank = It's not essential that I go to the bank.