"Must" and "have to" are both used to express obligation or necessity. "Must" is used for strong personal obligation or a strong recommendation, whereas "have to" is used for external obligations or rules. For example, "I must finish my homework before bedtime" conveys a personal obligation, while "I have to follow the company's dress code" conveys an external rule. Both "must" and "have to" are used to talk about the present and future, but "mustn't" is used to show prohibition, while "don't have to" is used to show lack of obligation in the present or future.