I have to go to work. I must go to work. Remember the 'to' before 'work'. Although you could also write it like this: I have to work. I must work. Anyway, there is not really a significant difference between the two.

There is a good explanation here, which provides lots of examples, and goes into a lot of detail: http://www.bbc.co.uk/worldservice/learningenglish/grammar/learnit/learnitv127.shtml

There is a significant difference. Must is personal obligation, have to, an external obligation. "You have to serve in the army in some countries" "I must do more exercise" The second is a personal goal, the first is a externally imposed obligation. Sometime the two categories coincide, however. "You must/have to renew your passport if you want to go abroad" But the emphasis is different- "must" stresses the personal (you need a new passport because you want to go abroad to visit your friends, perhaps) while "have to" emphasises the external obligation (the fact that you need to get the new passpost because its a legal requirement for foreign travel).

The meaning is pretty much the same.

have to - others forcing onto you must - self obligation