Difference in phrase usage

I kind of think 'have to' is a requirement from outside yourself while 'must do' is your own requirement. That's in the nature of a guess, so don't take it to the bank and try to cash it.

OK, I got this today from a Japanese English teacher, but it's not "official"...

I have to = I have (the chosen responsibility) to do this thing...
I must = I must (because I was directed to) do this thing...

Is this a (simplified but) true explanation?

No. The two expressions are almost interchangeable.

My mother told me that I have to do my homework before I can watch tv.

Could be. It's opposite of what I thought, but I was trying very hard to make a distinction. I trust Roberta more than myself on language usage.

"Have to" is a rephrase of "must," just like "be able to" is a paraphrase of "can" and "ought to" is a rephrase of "should."

In terms of meaning, they're the same; both are used to express types of modality. The difference between them is one of syntax. "Have to" doesn't belong to the modal family of verbs. Unlike "must," it has multiple forms.

OK, this has been pointed out to me on several English teaching pages on the Net. The Japanese English teacher did, in fact, have it backwards...

From English-Test.net:

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"Have to" and "must" have the same meaning in the affirmative and interrogative forms when referring to obligation. Some grammarians think that "must" is slightly stronger, but for all practical purposes, they mean the same thing:

Doctors have to attend medical school for several years before they can practice medicine.

Doctors must attend medical school for several years before they can practice medicine.

While "have to" and "must" can be used interchangeably, there are differences in usage, as Michael Swan observes in Practical English Usage (Oxford University Press, 1995):

Both verbs can be used in British English to talk about obligation. (In American English, 'have to' is the normal form.) British English often makes a distinction as follows. 'Must' is used mostly to talk about the feelings and wishes of the speaker and hearer — for example, to give or ask for orders. 'Have (got) to' is used mostly to talk about obligations that come from "outside" — for example from laws, regulations, agreements and other people's orders. Compare:

I must stop smoking. (I want to.)
I have to stop smoking. Doctor's orders.

This is a terrible party. We really must go home.
This is a lovely party, but we've got to go home because of the baby-sitter.

Must you wear dirty old jeans all the time? (Is it personally important for you?)
Do you have to wear a tie at work? (Is there a regulation?)

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'almost' being the operative word. 'must' is more formal and official and is often used when outside powers require certain behavior, eg. following the law, regulations etc.

'must' and 'have to' share the same degree of compulsion for the deontic modal sense [social] because they share the same epistemic [degree of certainty sense].

'have to' and 'have got to', the latter a stronger form both epistemically and deontically, are used more often than 'must' in informal day to day language.

It is true in some cases - the law compels us to do certain things, therefore we must do them - but it is also a bit misleading.