table game vs pool

table game and pool both are nouns.

Word	Noun	Adjective	Verb	Adverb
table game	Yes	No	No	No
pool	Yes	No	Yes	No

As nouns, pool is a hyponym of table game; that is, pool is a word with a more specific, narrower meaning than table game:

table game (noun)	pool (noun)
a game that is played on a table	any of various games played on a pool table having 6 pockets
	an excavation that is (usually) filled with water
	an association of companies for some definite purpose
	an organization of people or resources that can be shared
	something resembling a pool of liquid
	a small lake
	a small body of standing water (rainwater) or other liquid
	any communal combination of funds
	the combined stakes of the betters

table game (verb)	pool (verb)
	join or form a pool of people
	combine into a common fund