What is the difference between ‘mustn’t’ and ‘don’t have to’?

A. ‘Mustn’t’ indicates prohibition, while ‘don’t have to’ indicates lack of necessity.

B. ‘Mustn’t’ indicates permission, while ‘don’t have to’ indicates obligation.

C. ‘Mustn’t’ indicates necessity, while ‘don’t have to’ indicates possibility.

D. ‘Mustn’t’ indicates ability, while ‘don’t have to’ indicates probability.