Understanding modals must have to have got to

Prohibition: “You can’t eat these.”
Obligation: “I have to call home later.”
Necessity: “They must leave immediately.”
Permission: “Rachel can play outside if she likes.”
Ability: “My dog can swim.”

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.

All modals of necessity revert to “had to” in past tense; “must” and “have got to” do not have a past tense, despite some strange things that are occasionally heard in spoken English.

“Because the roads were bad, he had to leave early.”
“Beth had to get insurance for her new car.”

Must or Have To
These bossy modals both express an obligation but they differ in use; proper placement depends on the source of the requirement. Use “must” to indicate that the obligation comes from the speaker.

“You must stop by the next time you are in town.”
“I must stop eating so many cheeseburgers.”

“Have to” shows that the obligation comes from a source other than the speaker and cannot be changed, as it is some sort of rule, law or other iron-bound contract.

“We have to drive on the right, but others have to drive on the left.”
“David wanted to go to the party but would have to work that night.”

Have Got To vs Have To
Both are usable in present and future tense to express an obligation or a necessity, but “have got to” is more acceptable in British English than in American English.

Obligation: “I have got to get my wife some milk before I go home.”
Necessity: “Before you go fishing, you have got to get a license.”
Obligation: “They have to buy a pizza for Ray on their way back.”
Necessity: “I have to be home by midnight or I will turn into a pumpkin.”

“Have to” can be paired with an adverb that suggests repetition if you need to show an ongoing necessity in present and future tenses, such as “regularly” or “always.”

“I always have to wait in line whenever I go to that bank.”
“They regularly have to comfort the dog during storms.”

source grammar.net