"Must" or "have to" (less formal) is something that is necessary. "I must eat soon, or I will die." "I have to eat soon, or I will die." "Must"can also refer to something obviously being the only explanation for a certain situation. "Why does Joe act so strange around me?" "He must like you." "That sign says 'Exit 5'. It must be our exit." "Should" (less formal) or "ought to" refers to something that would bring about a better situation but is not necessary." "I should eat before the concert because food there will be expensive." "I ought to eat before the concert because food there will be expensive." It ought to be noted that these words are often used in incorrect ways for emphasis. For example: "I got two free tickets to see Paul McCartney in concert! You must come with me!!!" The person isn't legitimately obligated to go to the concert, but the friend is implying that it would be an absolutely horrible idea not to go.

Use "must" for rules and things that not negotiable. eg. You must stop at a red traffic light when driving. Use "should" for suggestions where there are options. eg. You should go to the party. "Must" can be seen as more rude but is clearer for giving instructions for rules and stating important or critical matters. "Should" is more polite in conversations about possible options and choices.

to add to previous answers, you can find a lot of articles like '10 movies you must see' or '100 things you must do in ...'. Of course there are no rules about great films to watch or things to do, in these cases 'must' is used for strong recommendation and it doesn't sound rude. 'you must see this movie' will be a stronger advice than 'you should see this movie'. this is why we have so many 'must-see'/'must-read'/'must-have' things.

They both are modal, must mostly is used for obligation ,while should is used for suggestion for example if we say : you must go (thats means you have to go ) you should go (thats means if you do that it will be your on your behalf ) but sometimes must can represent should you must watch this movie same meaing you should watch this film the differece is between them that you want to emphasize that dont miss this film :D