Must indicates necessity.
Example:
- I must leave now.
- He must study hard.
- Alex must go home by 6.00 pm.
Have to has the similar meaning to must but implies less urgency.
Example:
- I have to leave now.
- He has to study hard.
- Alex has to go by 6.00 pm.
- I had to leave then. (past)
- He had to study hard to pass the exam. (past)