"Should" versus "would"

Solution 1:

Smirkingman's answer is right but unhelpful. There are historically two different uses of "should", and kiamaluno is asking about the other one.

In older works you will find writers generally use "I/we should" where today most of us would write (and say) "I/we would", i.e. without any sense of obligation.

This is separate from the obligatory sense that smirkingman describes, and has no meaning different from "would".

There is a parallel with "shall" and "will" (and historically, "should" and "would" were the past tense of these): "Shall" has a sense of command - little used in speech today, but very much alive in legal documents and technical specifications; but for speakers of many varieties of English it is quite normal to say "I shall" as an alternative to "I will". For me at least "Shall I?" is the normal question form: I would only say "Will I?" when asking for a prediction.

Solution 2:

The trouble here is that should has many meanings depending on the context.

• It can imply obligation

  You should check your oil level.

• It can imply probability

  He should have finished checking the oil level by now.

• It can represent a condition

  If I should run out of oil, what then?

• It is the past tense of shall

  I told him he should have checked his oil level.

Nowadays, as your NOAD quote says, would is used where should used to be.

Consider "I should like a new car." This is valid but sounds old-fashioned. Here the use of should implies a kind of politeness: you're not presuming that you deserve a new car. Nowadays you'd more likely hear "I would like a new car" or the contracted "I'd like a new car."

Solution 3:

'should' implies that a constraint or obligation is anticipated:

I said I should be late.

It implies that there is something inhibiting my being on time or that I'll deliberately choose to be late.

'would' implies a degree of certainty:

I said I would be late.

I'm going to be late and that's it.

'could' implies possibility:

I said I could be late.

I'll try to be on time, but something might happen to prevent me.