woman vs fair sex

woman and fair sex both are nouns.

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

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

Other synonyms of woman include womanhood.

woman (noun)	fair sex (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