fair sex vs woman

fair sex and woman both are nouns.

Word	Noun	Adjective	Verb	Adverb
fair sex	Yes	No	No	No
woman	Yes	No	No	No

As nouns, fair sex and woman are synonyms defined as:

Other synonyms of fair sex include womanhood.

fair sex (noun)	woman (noun)
women as a class	women as a class
	an adult female person (as opposed to a man)
	a female person who plays a significant role (wife or mistress or girlfriend) in the life of a particular man