One Game is a single game between two teams. It is not part of a regular season or playoff series. One Game play can be between any two teams, regardless of what league or division they are in. A team can even play against itself.
League Playoffs are a best of 7 games series between the divisional champions in both leagues. The winner of a league playoffs series goes on to the League Championship.
The series is the best-of-seven-game championship playoffs between the A and N league champions in MLBPA baseball. When you choose The Series, one team from each league is chosen at random as league champion.
Full season sets up a complete MLBPA Baseball season. You can either play out the full season game by game or in sections (a day at a time, a week at a time, etc.). League playoffs follow the conclusion of a full season, and the Series follows the League Playoffs.
--From the SNES MLBPA Baseball instruction manual.