lyceum vs Gymnasium

lyceum and Gymnasium both are nouns.

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

As nouns, lyceum and Gymnasium are synonyms defined as:

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

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

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