How you word your explaination is up to you, but I lean towards "must" meaning rules, laws, strong obligations, and things that are vital for health and safety. "Have to", as I see it, means more general obligations and neccesary activities.
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Must VS Have to
A quick review of "must" vs "have to."
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It may be better and easier to describe 'must' as being more formal and less common in everyday speech.
"I have to go." - very common everyday parting phrase
"I must go." - only for comically dramatic departures