cologne vs cologne water

cologne and cologne water both are nouns.

Word	Noun	Adjective	Verb	Adverb
cologne	Yes	No	No	No
cologne water	Yes	No	No	No

As nouns, cologne and cologne water are synonyms defined as:

cologne and cologne water: a perfumed liquid made of essential oils and alcohol

Other synonyms of cologne include eau de cologne.

cologne (noun)	cologne water (noun)
a perfumed liquid made of essential oils and alcohol	a perfumed liquid made of essential oils and alcohol