Which is the correct sentence:
Will you wait for me?
Would you wait for me?
would sounds pretty polite.
They are both polite enough, in that sense there is no difference.
The difference in meaning is between the Future Indefinite ("will you") and subjunctive mood ("would you wait") is that in the former case the necessity for waiting is known to the speaker and the party whom the speaker is asking, whereas the latter ("would") suggests that the need for waiting is yet not certain, or even hypothetical.
Both sentences are "correct."
Would does indicate politeness/deference, and will can be used in "not certain" or "hypothetical" situations:
Will you wait for me if I asked you nice(ly)?
Would you wait for me if I asked you nice(ly)?
Here, would shows more deference ( ~= politeness). While, will, as usual when talking about future time, talks about the current resolve of the--in this case--the person being asked, to carry out a future action. It is neutral as far as deference/politeness.
As for your sentences, then, use would to be more polite/deferential.
'Would you wait for me?' is you trying to figure out if they'd do it.
'Will you wait for me?' is asking them to do it.