eau de cologne vs cologne

eau de cologne and cologne both are nouns.

Word	Noun	Adjective	Verb	Adverb
eau de cologne	Yes	No	No	No
cologne	Yes	No	No	No

As nouns, eau de cologne and cologne are synonyms defined as:

eau de cologne and cologne: a perfumed liquid made of essential oils and alcohol

Other synonyms of eau de cologne include cologne water.

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