It's regional coverage. Most of the country will receive NYM/NYY.
Percentages for 5/22/10 MLB on Fox:
NY Yankees @ NY Mets 54%
Chicago Cubs @ Texas 22%
Detroit @ LA Dodgers 13%
Boston @ Philadelphia 11%
It looks like from the link above that Reds country will get different games.
Cincinnati gets the Cubs/Rangers game. Columbus gets Yankees/Mets. Dayton will see Boston/Philadelphia.