academy vs middle school

academy and middle school both are nouns.

Word	Noun	Adjective	Verb	Adverb
academy	Yes	No	No	No
middle school	Yes	No	No	No

As nouns, middle school is a hypernym of academy; that is, middle school is a word with a broader meaning than academy:

academy: a secondary school (usually private)
middle school: a school for students intermediate between elementary school and college; usually grades 9 to 12

Other hypernyms of academy include Gymnasium, lycee, lyceum, secondary school.

academy (noun)	middle school (noun)
a learned establishment for the advancement of knowledge	a school for students intermediate between elementary school and college; usually grades 9 to 12
a secondary school (usually private)
a school for special training
an institution for the advancement of art or science or literature