The 1922 New York Giants created the first World Series ring after defeating the New York Yankees in five games.
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None of the players that played in the '95 Major League Baseball World Series regardless of being from the National League Champion; Atlanta Braves or the Cleveland Indians are currently playing with any of the Major League Baseball teams in 2014.
The World Series in baseball is the best team in the American League, playing the best team in the National League for the Major League Championship.
The ALDS is the American League Division Series. The ALDS and its National League equivalent, the NLDS, are the first rounds of Major League Baseball's postseason. There are 2 ALDS series. The winners meet in the ALCS (the American League Championship Series). Meanwhile the same happens in the NL. The ALCS and ALDS winners meet in the World Series.
The first major league in baseball was the National Association whose first year was 1871.
League Championships then the World Series
its the championship between the national league and American league champions
You did not mention at what level of baseball you are asking. But in every level there is a playoff system. Most levels from Little League to the Major League it is called the World Series. In the Major Leagues the World Series is determined by a best-of-seven game series between one American League team and one National League team. Whoever wins 4 games first wins the World Series.
The NFL
The lowest seed to win the World Series in Major League Baseball history is the 2003 Florida Marlins, who won as the wild card team.
Major League Baseball incorporated its first World Series in 1874. Contrary to popular belief, the 1903 Boston Americans-Pittsburgh Pirates postseason meeting was not the first World Series.
For the American League the pennant winners were the Chicago Whitesox. (This was the first year the AL was elevated to Major League level. For the National League the pennant winners were the Pittsburg Pirates. No World Series was held this year.