Today from Grammar.net, modals of necessity.
Modals of Necessity There are three: have to, have got to and must. When these appear, they show that something is necessary and not an option. They can illustrate a one-time or recurring requirement.
“Must” is the most powerful, it is most often used in writing and it is rarely found in questions. “Have got to” is more common in conversation, it is never found in questions, and “got” can be emphasized when spoken to show drama. “Have to” is the most favored for questions, it is useful for forming negatives, and it is the most common of these three modals.
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Source: Understanding modals of necessity from Grammar.net.