lady of the house vs woman of the house

lady of the house and woman of the house both are nouns.

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

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

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

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

lady of the house (noun)	woman of the house (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