field hockey vs field game

field hockey and field game both are nouns.

Word	Noun	Adjective	Verb	Adverb
field hockey	Yes	No	No	No
field game	Yes	No	No	No

As nouns, field game is a hypernym of field hockey; that is, field game is a word with a broader meaning than field hockey:

field hockey: a game resembling ice hockey that is played on an open field; two opposing teams use curved hockey sticks try to drive a ball into the opponents' net
field game: an outdoor game played on a field of specified dimensions

field hockey (noun)	field game (noun)
a game resembling ice hockey that is played on an open field; two opposing teams use curved hockey sticks try to drive a ball into the opponents' net	an outdoor game played on a field of specified dimensions