Both "would" and "should" are modal verbs. They are used as auxiliary verbs in order to complete the meaning of the sentence together with the main verb.
Nevertheless, they have completely different meanings.
-"Would" is used to express possibilites or hipotetical situations (e.g. "If I had a lot of money, I would spend it all at making the world a better place) and to ask or offer something politely (e.g. "Would you please help me learn other languages?").
-"Could" is also used to express possibilities and ask things politely, but with the meaning of affirming or questioning the concrete possibility of something. (e.g. "If I gave my car keys right now, could you drive it?" or "The door bell just rang. It could be Claire" or "Could you please move your chair, mister?"