HELP sheet - Must or Have to? An explanation
In the affirmative both express an obligation:

"I must go now" "I have to go now"- both are correct.

The big difference is in the negative:

"Don't have to" permits, "Mustn't" forbids (It's used a lot with children!):

Permissive:
"You don't have to wear a mask in the shop." (But you can if you wish.)
"You don't have to drive." (You could take the bus.)
Prohibitive:
" You mustn't enter the hospital without a mask." (It's dangerous and therefore forbidden.)
" You mustn't drive down there!" (It's a one-way street.)
"Johnny! You musn't touch the electric fire! You'll burn yourself."

In the affirmative, however, "Must" and "Have to" have a more nuanced difference in usage:

Must is more an internal obligation coming from the speakers motives or feelings.

"I must give more to charity this year." (I'm feeling guilty.)
"I really must get a new cooker." (This one is not convenient.)
" I must get an appointment at the dentist." (I have toothache).

Have to is more an external obligation imposed from the outside.

"I have to give more to charity next year." (My accountant says there's a tax advantage.)
"The electric people say I have to get a new cooker because the one I've got is dangerous."
"I had to make a dentist's appointment on the internet." (he no longer answers phone calls)

Often the motive is not expressed but can be inferred:

"Must I wear a tie?" (I hate ties)
"Do I have to wear a tie?" (at your wedding where you make the rules)

Deduction or inference is another use of Must - in the affirmative:

"He has a Rolls Royce so he must be rich."
"That man has a tattoo of an anchor on his arm." He must have been in the Navy.

N.B. A negative inference, curiously is not usually expressed with must not but with can not:

"That can't be true. It's just something you've seen on the internet!"
"The dog can't have killed the hens. He was locked in the house at the time."