Will states your own plan or a confident prediction. Should names what is right, expected, or advised. The first commits you to a course of action, while the second leaves the decision open to change.
Paired sentences
I will send it Friday. You have decided. The message reads as a commitment, and the reader can plan around it.
I should send it Friday. You are telling yourself what the right move is. The plan is still up for negotiation.
The courier will arrive before noon. You are predicting. You are confident enough to state it as fact.
The courier should arrive before noon. You are expecting it, with room for surprise. This is the same slot, hedged. Choose it when traffic, weather, or your own uncertainty softens the claim.
I won't argue with the refund. Here won't shows refusal, which is willingness running in the negative. The reader hears a firm position on your part.
You should rewrite the second paragraph. You are advising, and the decision still belongs to the reader. In a formal review the same sentence reads as an instruction; between equals, it reads as a suggestion.
Where the choice gets harder
The paired sentences already show the overlap in expectations, so here is the one place where the two words genuinely differ in a message.
In questions, the choice changes what you are asking. Should I send it Friday? asks for advice. You want the reader to say whether Friday is the right day, and the decision stays open.
Will I send it Friday? is a prediction question. It treats Friday as a settled fact and mostly sounds like you expect someone else to know your own future. That rarely matches what a message needs.
So when you want guidance, reach for should. Will fits only when the answer genuinely belongs to the other person, as in Will you be at the office Friday?, where you are asking about their plans rather than yours.