player vs server

player and server both are nouns.

Word	Noun	Adjective	Verb	Adverb
player	Yes	No	No	No
server	Yes	No	No	No

As nouns, server is a hyponym of player; that is, server is a word with a more specific, narrower meaning than player:

player (noun)	server (noun)
a theatrical performer	utensil used in serving food or drink
a person who participates in or is skilled at some game	(computer science) a computer that provides client stations with access to files and printers as shared resources to a computer network
someone who plays a music as a profession	a person whose occupation is to serve at table (as in a restaurant)
a person who pursues a number of different social and sexual partners simultaneously	(court games) the player who serves to start a point
someone who takes part in an activity