pool vs swimming bath

pool and swimming bath both are nouns.

Word	Noun	Adjective	Verb	Adverb
pool	Yes	No	Yes	No
swimming bath	Yes	No	No	No

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

Other hyponyms of pool include cistern, natatorium, swimming pool, wading pool, water jump.

pool (noun)	swimming bath (noun)
any of various games played on a pool table having 6 pockets	pool that provides a facility for swimming
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)	swimming bath (verb)
join or form a pool of people
combine into a common fund