Would is a verb
1. past of will, in various senses.
Example: "he said he would be away for a couple of days"
2.(expressing the conditional mood) indicating the consequence of an imagined event or situation.
Example "he would lose his job if he were identified"
Should is an auxiliary verb
1.simple past tense of shall.
2.(used to express condition):
Example:Were he to arrive, I should be pleased.
3.must; ought (used to indicate duty, propriety, or expediency):
Example: You should not do that.
4.would (used to make a statement less direct or blunt):
Example: I should think you would apologize.