apartment house vs apartment building

apartment house and apartment building both are nouns.

Word	Noun	Adjective	Verb	Adverb
apartment house	Yes	No	No	No
apartment building	Yes	No	No	No

As nouns, apartment house and apartment building are synonyms defined as:

apartment house and apartment building: a building that is divided into apartments

apartment house (noun)	apartment building (noun)
a building that is divided into apartments	a building that is divided into apartments