swimming bath vs swimming pool

swimming bath and swimming pool both are nouns.

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

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

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

Other synonyms of swimming bath include natatorium.

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