ESL students who have learned English in their own countries sometimes ask me about which is 'stronger' - 'must' or 'have to'.

It seems odd to me that this question should come up. The terms are different when we make them negative (must not, don't have to), and when we start changing the tenses (must have..., had to) of course. 'Must' might be preferred in written English. But surely they have exactly the same 'strength' (at the top of a list that goes; must/have to, had better, should/ought to, might/could)?

Am I missing something? Did they use to have different meanings?

The modal verb must is a strange one. The "t" on the end of it indicates an ending which was originally past tense in meaning. The word later acquired a present-tense meaning, so that it was felt a new past-tense form having nothing to do with the original was required.

Had to is what is called a suppletive form. That is, it functions as the past tense of a verb from an entirely different root. We can hardly dispense with this in modern English, unless we were to say, "Well, John felt he musted do it, under the circumstances," instead of what we do say, "John felt he had to do it under the circumstances." The possible double past-tense form "musted" was early on ruled out as ugly or whatever.

With less obvious disturbance to language patterns, the verb "go" is another example of a verb with a suppletive past tense, namely went. The original present tense wend has become differentiated, and survives perhaps only as an archaism in expressions such as "to wend one's way through the daisies."

"To have (to)" meanwhile, has gone the opposite direction, and has acquired, in one of its many senses, the same meaning as "must."

I'm not sure if any of this language history will make your students any happier, but that's the way it happened, more or less, and we're stuck with the results, as illogical as they may seem.