highschool vs lycee

highschool and lycee both are nouns.

Word	Noun	Adjective	Verb	Adverb
highschool	Yes	No	No	No
lycee	Yes	No	No	No

As nouns, lycee is a hypernym of highschool; that is, lycee is a word with a broader meaning than highschool:

highschool: a public secondary school usually including grades 9 through 12
lycee: a school for students intermediate between elementary school and college; usually grades 9 to 12

Other hypernyms of highschool include Gymnasium, lyceum, middle school, secondary school.

highschool (noun)	lycee (noun)
a public secondary school usually including grades 9 through 12	a school for students intermediate between elementary school and college; usually grades 9 to 12