stately home vs mansion house

stately home and mansion house both are nouns.

Word	Noun	Adjective	Verb	Adverb
stately home	Yes	No	No	No
mansion house	Yes	No	No	No

As nouns, mansion house is a hypernym of stately home; that is, mansion house is a word with a broader meaning than stately home:

stately home: a mansion that is (or formerly was) occupied by an aristocratic family
mansion house: a large and imposing house

Other hypernyms of stately home include hall, manse, mansion, residence.

stately home (noun)	mansion house (noun)
a mansion that is (or formerly was) occupied by an aristocratic family	a large and imposing house