Asking a native speaker is the worst thing you can do if you want to get precise information on the grammar of any language (unless such a person is a linguist, of course). Native speakers take their language as something "natural", they don't really think about the construction and linguistic meaning of their sentences. This MUST and HAVE TO thing is a good example of that. The difference between these has absolutely nothing to do with importance of what is to be done, as SR suggested, although it might actually seem so in lots of cases. The "truth" is as follows:

There are two fundamental meanings of MUST and HAVE TO - the first is used in cases when the speaker wants to express a necessity or obligation to do something. Now if it's an obligation or necessity caused by external circumstances (e.g. provision of law, prior promise, a need to get some information, the situation itself, etc), we have to use HAVE TO. It's also useful to remember that questions with MUST aim for wishes or intentions of the person asked.
Compare these sentences and think about if the MUST could be replaced with HAVE TO or vice versa:
Some day I must ask him why he did it.
I'm sorry, but I must insist on an answer.
You can go there, but you must be home by six.
Walter's the expert. We'll have to ask him how it works.
I have to laugh when I think about it now.
Must you leave so early? --- I'm afraid I have to.

The second meaning is used when we are sure of something, since it can be logically derived from a particular situation. Here, we have to use MUST.
What a marvellous offer, he must be very generous.
You must be crazy to want to marry her!
I always know what I want. --- That must be nice.
Romantic music must have shocked its first listeners.