Johnny, these words are very similar. Both words are "auxilliary verbs". "Should" is the Past Tense of "Shall". Technically "should" is a synonym of "must", but it is not usually used that way, at least not in the U.S. 'Should" indicates duty or propiety, an is used to strongy suggest that something be done. "Must" is stronger and indicates an imeritive requirement, and is used to command or insist that something be done. Example: "You should wear a hat" = I strongly suggest that you wear a hat, but you can choose. "You must wear a hat" = You are obligated to wear a hat. You have no choice.

must and should are modal verbs, they need another verb to function must is used to say that sth is necessary or very important (sometimes involving a rule or a law eg All visitors must report to reception. Cars must not park in front of the entrance (= it is not allowed) should is used to show what is right, appropriate, etc., especially when criticizing sb’s actions: eg; You shouldn’t drink and drive. He should have been more careful. it is also used for giving or asking for advice: eg: You should stop worrying about it Should I call him and apologize?

"should" expresses a piece of advice, a recommandation "you should get some rest" (that's my opinion, I'm advising you) it's your choise to do or no but must it's better to do "must" expresses an obligation: "you must get some rest" (you have to, you are obliged to)

It's a quite big topic. There are too many situations. I recommend reading "modal verbs" in grammar refference book.

İf you use "should" ,you give advice someone like friends or sister it is more informal than "must" but if you use "must" - it is not friendly - the stuation is formal and you can get reaction from people if you don't do what have told you.It includes necessity.