Modal verb sollen

Differences between sollen and müssen

The modal verb müssen expresses a necessity in general, while sollen expresses a necessity that is the result of a request/command addressed to the subject of the verb.

Examples
Paul soll morgen Überstunden machen.	a. because his boss has asked him to.	necessity (request/command)
Paul muss morgen Überstunden machen.	b. because he wants to finish his project.	necessity
	c. because he needs money.	necessity
	d. because he was sick today.	necessity

This means that müssen contains the meaning of sollen, it is, however, not clear that it involves a request/command. If the aspect of "request/command" is important to what is being said, it has to be clarified by the context.

Examples
Paul muss morgen Überstunden machen, weil das sein Chef von ihm verlangt hat.	=	Paul soll morgen Überstunden machen.

If what is being said contains the aspect of request/command, according to context, sollen can be replaced by müssen.

There is also a difference in the intensity of the necessity. Müssen expresses a strong necessity that cannot be overlooked without consequences.

Example	meaning	intensity of necessity
Du sollst einkaufen gehen!	Du wirst von mir/uns/jdm. aufgefordert, einkaufen zu gehen.	+
Du musst einkaufen gehen!	Du hast keine Wahl. Wenn du es nicht tust, gibt es Folgen.	+ +