mansion vs stately home

mansion and stately home both are nouns.

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

As nouns, stately home is a hyponym of mansion; that is, stately home is a word with a more specific, narrower meaning than mansion:

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

Other hyponyms of mansion include manor, manor house, castle, palace, mcmansion.

mansion (noun)	stately home (noun)
a large and imposing house	a mansion that is (or formerly was) occupied by an aristocratic family
(astrology) one of 12 equal areas into which the zodiac is divided