difference between a proxy and an absentee balott in New York residential coop bylaws?

Answer 1

A proxy is someone who votes in your place. An absentee ballet is one on which you vote when you cannot be present at the place and time of voting.

Answer 2

With a proxy, you are authorizing someone else to vote in your place - they can decide how to vote. With an absentee ballot, you actually do the voting, you just aren't there when the vote is taken.