bathing vs shower bath

bathing and shower bath both are nouns.

Word	Noun	Adjective	Verb	Adverb
bathing	Yes	No	No	No
shower bath	Yes	No	No	No

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

bathing: the act of washing yourself (or another person)
shower bath: washing yourself by standing upright under water sprayed from a nozzle

Other hyponyms of bathing include shower, bath, sponge bath, steam bath, Turkish bath, vapor bath, vapour bath.

bathing (noun)	shower bath (noun)
immersing the body in water or sunshine	washing yourself by standing upright under water sprayed from a nozzle
the act of washing yourself (or another person)	booth for washing yourself, usually in a bathroom