Must is used to talk about certainty in the past and to express something that is prohibited or not allowed. Have to expresses obligation or necessity in the present or future. While must and have to can both express certainty, they have different meanings in the negative - must indicates something is prohibited while have to expresses a lack of obligation.

2. Must vs Have to

3. To speak about certainty in the past, we use must:
•He must have been late because I saw him miss the train.
•The storm must have spoilt their picnic.
It is not possible to use have to this way.
Also, must and have to can both be used to
express the idea of certainty:
He must be the fastest swimmer in the world.
He has (got) to be the fastest swimmer in the world.

4. When used in the negative, must and have to have
different meanings. Must is used to say that something
is prohibited, while have to is used to express a lack of
obligation:
• You mustn't cross the road here. (It is prohibited)
• You don't have to cross the road here. (It's not necessary, i.e.
you can stay on this side and cross later).