Differences Should/Must

Should

It is used to give advice, such as "should" in Spanish. It's a way of expressing advice fairly directly, and there are ways that are considered friendlier. Compare the following examples:

-You should make sure your safety equipment is in good condition before entering.

-You might want to add some color to that.

-Would not you rather finish this now so you can rest later? 

Must

It is used to express a restrictive obligation. The difference with "should" is quite clear, since here we are not expressing a council but an internal order, norm or obligation. Here are some examples:

-I must do this on my own.
-Books must be returned to the library where they were borrowed. 
-You must never speak of this again.