I keep struggling to understand the difference between WOULD and SHOULD.
I saw in a book two examples of cover letter:
1) I was very interested to.... and would like to be considered for this post.
2) I was very interested to.... and should like to be considered for this post.
Which is the difference?
It all gets back to the question of will vs shall. And you could (and many have) fill a book on that question.
In the case you have cited above, the "should" form would only be used in written English, and then as a "softening" word. It simply sounds a bit more polite, less agressive. The connotation is almost insignificant, however. No one would consider the first phrase impolite or agressive. And that format, the "would" format, is what you would say, in spoken conversation.
The other usages of should imply dictation / direction /command. "You should not blow your nose on your sleeve." To use would in that sentence changes it to assurance you certainly know better already: "You would not blow your nose on your sleeve; why the, would you use the tablecloth?"
Or as assurance. "I think I'd like to see that movie." "You should! It's really great!" It's not a command, just an endorsement of your idea.
I'll stop now, or I'll have to get a publisher for my book!