Gymnasium vs lyceum

Gymnasium and lyceum both are nouns.

Word	Noun	Adjective	Verb	Adverb
Gymnasium	Yes	No	No	No
lyceum	Yes	No	No	No

As nouns, Gymnasium and lyceum are synonyms defined as:

Gymnasium and lyceum: a school for students intermediate between elementary school and college; usually grades 9 to 12

Other synonyms of Gymnasium include lycee, middle school, secondary school.

Gymnasium (noun)	lyceum (noun)
a school for students intermediate between elementary school and college; usually grades 9 to 12	a public hall for lectures and concerts
	a school for students intermediate between elementary school and college; usually grades 9 to 12