gynaecologist vs woman's doctor

gynaecologist and woman's doctor both are nouns.

Word	Noun	Adjective	Verb	Adverb
gynaecologist	Yes	No	No	No
woman's doctor	Yes	No	No	No

As nouns, gynaecologist and woman's doctor are synonyms defined as:

Other synonyms of gynaecologist include gynecologist.

gynaecologist (noun)	woman's doctor (noun)
a specialist in gynecology	a specialist in gynecology