pool vs table game

pool and table game both are nouns.

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

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

pool (noun)	table game (noun)
any of various games played on a pool table having 6 pockets	a game that is played on a table
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

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