woman of the house vs housewife

woman of the house and housewife both are nouns.

Word	Noun	Adjective	Verb	Adverb
woman of the house	Yes	No	No	No
housewife	Yes	No	No	No

As nouns, woman of the house and housewife are synonyms defined as:

woman of the house and housewife: a wife who manages a household while her husband earns the family income

Other synonyms of woman of the house include homemaker, lady of the house.

woman of the house (noun)	housewife (noun)
a wife who manages a household while her husband earns the family income	a wife who manages a household while her husband earns the family income