swimming pool vs swimming bath

swimming pool and swimming bath both are nouns.

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

As nouns, swimming pool and swimming bath are synonyms defined as:

swimming pool and swimming bath: pool that provides a facility for swimming

Other synonyms of swimming pool include natatorium.

swimming pool (noun)	swimming bath (noun)
pool that provides a facility for swimming	pool that provides a facility for swimming