In English, there is clear difference in the meaning of the following expressions:
must know the lawneed to know the ruleshave to know the recommendationsBut in German, as far as I can see from Google Translate, all these three phrases are translated with the verb müssen. Is it true or in German there are also the different degrees of freedom (must < need to < have to)?
Müssen is most common; e.g. Ich muss zur Schule gehen.
Jemand hat etwas zu tun implies somebody makes you do it or dictates you do it:
Sie haben nicht zu fragen, sondern zu gehorchen.
Need to would be translated as brauchen, as in
Ich brauche einen Stift / I need a pen.
In this form it's least strong and more a request or desire. I need to leave now would be translated with müssen.
So: brauchen < müssen < etwas zu tun haben
I am not sure the difference is all that clear (and sometimes simply a matter of personal preference) but yes, in most of these cases you'd use the German muss.
You can, of course, reword (es ist notwendig / zwingend / verpflichtend zu ...) and have to is used literally (hat zu) as well:
Der Verkehrsteilnehmer hat sich an die Straßenverkehrsordnung zu halten.
"müssen" is more like an informal word in German. It always has a simple, even childish or naive touch to it, more so when it is used without a verb, like so:
"Ich muss aufs Klo." = "I need to go to the toilet"
"Ich muss in die Schule." = "I have to go to school"
Other examples:
"Ich muss Hausaufgaben machen." = "I've got homework to do."
"Ich muss jetzt Fernsehen gucken." = "I (strongly, absolutely) want to watch TV now."
"Ich muss jetzt was trinken." = "I'm so thirsty."
"Ich muss nicht zur Schule gehen." = "I don't need to go to school." (Remember this: "Ich muss nicht ..." is not "I must not" but "I don't have to")
In slightly more formal or polite contexts, we weaken "müssen" with some other construction, mostly conjunctives like:
"Ich müsste mal Ihre Toilette benutzen." = "Sir, I would need to use your toilet."
"Du solltest öfter deine Hausaufgaben machen." = "You should do your homework more often."
"Es wäre schön, wenn du das Fenster aufmachst." = "It would be nice if you open the window."
"Du brauchst nichts zu sagen." = "You don't need to say anything."
(Compare "Du musst nichts sagen." = More impolite version.)
In official contexts, much is done to avoid the word "müssen". Complicated constructions are used for this.
For example: "haben zu" is pretty much never used in informal contexts.
So, long story short: In German it's not so much about the exact meaning, but about politeness and formal or informal contexts. There are many nuances depending on what you say to whom and where and in what context, especially in case of "müssen".
A typical reaction of a German, when you use "Du musst ...", and he or she finds its usage impolite is: "Ich muss gar nichts." (= "I don't have to do (anything).")
In English, a clear distinction is made between must and other verbal forms that are used to indicate requirements. In German, this distinction is not so strict.
For example, in contracts, standards, and technical documents written in English, the verbal form shall is used to indicate requirements strictly to be followed in order to conform to the document and from which no deviation is permitted. In order to avoid any confusion between the requirements of the document and external statutory obligations (i.e. laws), the verbal form must is not used as an alternative for shall. However, the corresponding German-language documents translate shall as müssen.
