schoolhouse vs building

schoolhouse and building both are nouns.

Word	Noun	Adjective	Verb	Adverb
schoolhouse	Yes	No	No	No
building	Yes	No	No	No

As nouns, building is a hypernym of schoolhouse; that is, building is a word with a broader meaning than schoolhouse:

schoolhouse: a building where young people receive education
building: a structure that has a roof and walls and stands more or less permanently in one place

Other hypernyms of schoolhouse include edifice.

schoolhouse (noun)	building (noun)
a building where young people receive education	the act of constructing something
	the commercial activity involved in repairing old structures or constructing new ones
	a structure that has a roof and walls and stands more or less permanently in one place
	the occupants of a building