academy vs honorary society

academy and honorary society both are nouns.

Word	Noun	Adjective	Verb	Adverb
academy	Yes	No	No	No
honorary society	Yes	No	No	No

As nouns, academy and honorary society are synonyms defined as:

academy and honorary society: an institution for the advancement of art or science or literature

academy (noun)	honorary society (noun)
a learned establishment for the advancement of knowledge	an institution for the advancement of art or science or literature
a secondary school (usually private)
a school for special training
an institution for the advancement of art or science or literature