are the mets and the yankees in the same league
The Mets--Yankees rivalry refers to the latest incarnation of the Subway Series, which is the interleague rivalry between New York City's Major League Baseball (MLB) teams: the New York Mets and the New York Yankees. The Mets are a member club of MLB's National League (NL) East division, and the Yankees are a member club of MLB's American League (AL) East division.
Mets–Yankees rivalry