These words are all used for obligations – things that are necessary and required.
Must is the most formal. It is usually used in official rules (and is not as common in spoken English):
NEVER use the word “to” after must. “Must to” does not exist!
In everyday English, need to, have to, and got to (informal) are more common ways of expressing obligations:
When talking about actions you need to do, ALWAYS use the word “to” after need/have and before the verb:
When spoken fast:
Be careful when using the negative form. Mustn’t is different from “don’t need to” and “don’t have to.” Mustn’t means something is prohibited/forbidden, but “don’t need to” and “don’t have to” mean something is not required; it is optional.