This question is not a duplicate of:
because it provides detailed dictionary definitions, reveals a likely contradiction in the strength of these two words, and covers usage scenarios that are not addressed by those questions.
The definitions of shall and should confused me. It seems that shall can be either stronger or weaker than should.
Case 1: shall < should
modal verb (SUGGEST)
used, with "I" or "we", to make a suggestion:
Shall I call him tomorrow?
modal verb (DUTY)
used to say or ask what is the correct or best thing to do:
Should I apologize to him?
Case 2: shall > should
modal verb (CERTAINLY WILL)
used to say that something certainly will or must happen, or that you are determined that something will happen:
You shall go to the ball, Cinderella.
modal verb (PROBABLE)
used to show when something is likely or expected:
You should find this guidebook helpful.
So if two senior people (for example, a shall boss and a should boss) tell me:
You shall do something. and You should do something., or
The work shall be done tomorrow. and The work should be done tomorrow.
How can I tell who has a stronger will?