"have to"는 좀 무레한 표현이에요.

예) You have to go to work. (예의 없이)
예) You must go to work ("안 가 면 죽었어요"라고 빨리 가야되는 뜻)
예) You should go to work (사무실에 가야돼요)

It also depends on who is speaking to whom. 좀 복잡하죠? 보통 "have to" 보다 "should"가 더 사용해요. 상황마다 달라요.

To answer the later question first, we do use the word 'must'.
Now, the harder of the two to answer.
The words must and have to are very similar, so that is a tough question to answer.
Thinking about it I think they really are the same, the only difference is that must can also be used to describe a place.

Example: "It is very musty in here."
But that is a totally different use of the word then what you are asking about.

Most of the time you could use either.
Example ( have to ): "My mom told me I have to clean out the garage."
Example ( must ): "My mom told me I must clean out the garage."

Example 2 ( have to ): "You have to do your homework later!"
Example 2 ( must ): "You must do your homework later!"

As you can see in a lot of situations, the words are interchangeable.
However, there are some phrases where interchanging the words wouldn't work.

Must: "That book is a must read!"
Have to: "That book is a have to read!"

You could obviously change around the sentence so that it would make sense, but it wouldn't be the same phrase.

I really hope that helps. ^ ^ Tell me if you have any more questions.

Oh, I also agree with Matthew. A lot of times you should use the word 'should'.

It also depends on who is speaking to whom.
Both 'must' and 'have to' are quite commanding. You wouldn't tell your friend that they 'have to' do anything. However, it is perfectly fine for your mother to tell you that you 'must' clean the dishes after dinner.

matthew254さんはどうして韓国語で書きましたか?英語で書いてもいいですよ。＾＾

そして、hanyamon-3さんが日本人ですから韓国語で書ければ分かるかな。

when you have to do something, this is because the law tells you so, or because there is something that makes you obey the rule
I have to waer a uniform at school.
when you must do something, it usually may have 2 meanings:
1) it's your logical assumption
You look just like David. You must be brothers! (=I'm sure you are)
2) it's something which you tell yourself to do, so it's not really necessary
I'm hungry, I must eat something! (=I think I should eat something)