Must is a modal auxiliary verb.
Have to is NOT an auxiliary verb (it uses the verb have as a main verb). We include have to here for convenience.
In this lesson we look at these two verbs, followed by a quiz to check your understanding:
Grammar Verbs Passive voice Modal verbs Conditionals Questions Irregular verbs Going to Gerunds Phrasal Verbs Tenses Nouns (Un)Countable nouns Adjectives Articles Pronouns Preposition List