gym vs gymnasium

gym and gymnasium both are nouns.

Word	Noun	Adjective	Verb	Adverb
gym	Yes	No	No	No
gymnasium	Yes	No	No	No

As nouns, gym and gymnasium are synonyms defined as:

gym and gymnasium: athletic facility equipped for sports or physical training

gym (noun)	gymnasium (noun)
athletic facility equipped for sports or physical training	athletic facility equipped for sports or physical training