Gymnasium vs secondary school

Gymnasium and secondary school both are nouns.

Word	Noun	Adjective	Verb	Adverb
Gymnasium	Yes	No	No	No
secondary school	Yes	No	No	No

As nouns, Gymnasium and secondary school are synonyms defined as:

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

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

Gymnasium (noun)	secondary school (noun)
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