When I see examples of 'must' or 'will' showing certainty, I find that the main verb is either a stative verb or a present participle preceded by 'be'. How different are the two sentences in the following pairs:
He will be coming. VS He will come.
He must be working. VS He must work.
Wikipedia has reasonably good coverage of modal verbs.
Must is stronger than will: must indicates a requirement, whereas will indicates a prediction of future action without regard to its cause. If someone will do something, we don't know whether it's because they have to, or they want to, or it's just a matter of circumstance.
See also RFC 2119 which outlines the specific meanings of the modal verbs MUST, MAY, SHOULD, and SHALL in requirements documents that cite RFC 2119.
The two phrases with must are actually quite different.
He must be working:
I am expressing certainty that he is currently working.
He must work:
In general, work is something he has to do.
The two phrases with will are similar, with only a subtle difference.
He will be coming:
I am expressing certainty that he will come, and am considering that action (of him coming) as continuous; that is, I am thinking of it happening over some time period.
This suggests certainty that his transit will occur.
He will come:
I am expressing certainty that he will come, and am considering that action (of him coming) as discrete; that is, it is one complete action in my mind.
This suggests certainty that his arrival will occur.
The word 'must' in many cases seems to me as lacking of a choice in the matter, like 'have to'. My more used word 'will' allow freedom of choice.
