Hi,
“Should” means that you think you probably need to do something while “must” means you definitely have to do it.
For example, I “should” go to class today. This means that I really feel that I need to go but if I don’t it’s okay.
I “must” go to class today. This has a stronger meaning. It means that you definitely will have to go to class today because it is mandatory or there may be some consequence if you don’t go.
In the end, they both mean an action that needs to be done but “must” is a definite need to do it while should is more of a weaker need to do something. (Side note, many times “should” is used based on FEELING the need to do something or ADVISE on how to do something)
I hope this helps.