MUST:

• Laws

 You must stop for the red light

• When something is logical

 It must be nice to live in a big house.​

 

HAVE TO:​

Can be used instead of must except for in laws and logic.

​

However, in their negative forms, mustn't and don't have to have completely different meanings: 

•  Mustn't expresses that something is forbidden: 

You mustn't drive. You are prohibited to drive. You are not allowed to drive.

You mustn’t talk about this, it’s a secret.
•  Don't have to means that it is not necessary:

You don't have to drive. You are not obliged to drive (but you can if you want to).

You don’t have to come

 He doesn’t have to sign

 We didn’t have to come in early

​

MUST IN ALL TENSES:

MUST ONLY HAS A PRESENT TENSE FORM. IN ALL OTHER TENSES YOU USE HAVE TO  (have to is not an auxiliary):

​

Yesterday I had to go to the dentist. 

Did you have to go to the dentist yesterday?

I didn't have to go to the dentist yesterday.

​

You have had to go to the dentist a lot lately.

Have you had to go there often lately?

I haven't had to go there often lately.

​

Tomorrow I will have to be at school early.

Will you have to be at school early tomorrow?

I won't have to be at school early tomorrow. 

​