I don't think that english.stackexchange.com/questions/5902/ is relevant, but /12458/ does a good job of explaining the difference. It's more than Brake wants to know, though.
These two words change meaning in different contexts. E.g., if I want someone to close the door, I can use either one and mean the same thing: "{Could / Would} you close the door (, please)?" It can be construed as a polite request (more polite than "Will you...?") or as an order if, for example, I'm talking to a subordinate (a child, my child, a student and I'm the teacher, an interviewee and I'm the interviewer).
While they both are used to express hypotheticals, they are also the past tenses of the modals "can" and "will", respectively. Therefore, it seems natural to me (an American-speaker) to say:
- John says he can come to the party tonight.
- John said he could come to the party tonight.
Both mean that John has free time and transportation. Nothing is preventing him from coming to the party.
- John says he will come to the party tonight.
- John said he would come to the party tonight.
Both mean that John intends to come to the party.
The difference between the two odd sentences and the the two even sentences is that there is concord (agreement) in tense.
Another possibility is this:
- John said that he could come to the party but would come only if Mary would be there.
John doesn't know whether Mary is going to be there, so he's expressed a conditional: "I will come only if Mary comes too."
- John said that he could come and that if Mary were going to be there, he would come, but that because she was in a coma in the hospital, he wouldn't come.
Nothing is preventing John from coming to the party (he has time and transportation, so he can/could attend the party). If his condition were going to be met (Mary is coming to the party too), he also would come, but now that he knows that Mary's in a coma, her attendance at the party is a hypothetical, so he won't come.
I may have missed some other possibilities, but this should be sufficient to explain what Brake wants to know.