Difference between must and have to?

[ngoc]

Test No. incompl/elem-7 "Modals", question 3

I ......... go now because I am already late for my class.

(a) must
(b) have
(c) have to

Test No. incompl/elem-7 "Modals", answer 3

I have to go now because I am already late for my class.

Correct answer: (c) have to
_________________________

What is the difference between "must" and "have to"?

[Torsten]

We use have to if we want to express an objective obligation, that means something is obligatory, for example:

My father has to work 8 hours every day.
You have to study at university if you want to obtain my MBA.

We use must to express a subjective obligation. A subjective obligation is something essential or nessary, for example:

I must leave now. or You must come to our party. (you simply can't afford missing it).

TOEIC short conversations: Two employees talk about the transfer of one of their co-workers