high school vs lycee

high school and lycee both are nouns.

Word	Noun	Adjective	Verb	Adverb
high school	Yes	No	No	No
lycee	Yes	No	No	No

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

high school: 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 high school include Gymnasium, lyceum, middle school, secondary school.

high school (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