Degree of Politeness Auxiliary
somewhat polite: "Could you tell me ...?"
quite polite: "Would you tell me ...?"
The modal auxiliary
could is used
[1] to express an ability in the past:
ex: I could always beat you at tennis when we were kids.
[2] to express past or future permission:
ex: Could I bury my cat in your back yard?
[3] to express present possibility:
ex: We could always spend the afternoon just sitting around talking.
[4] to express possibility or ability in contingent circumstances:
ex: If he studied harder, he could pass this course.
Note that, in expressing ability,
can and
could frequently also imply willingness: Can/Could you help me with my homework?
"could" Source
The modal auxiliary
would is used
[1] to express willingness:
ex: Would you please take off your hat?
[2] to express insistence (rather rare, and with a strong stress on the word "would"):
ex: Now you've ruined everything. You would act that way.
[3] to express characteristic activity:
ex: After work, he would walk to his home in West Hartford. <customarily>
ex: She would cause the whole family to be late, every time. <causal>
[4] to express a hypothetical meaning:
ex: My cocker spaniel would weigh a ton if I let her eat what she wants.
[5] to express a sense of probability:
ex: I hear a whistle. That would be the five o'clock train.
"would" Source