schoolmate vs classmate

schoolmate and classmate both are nouns.

Word	Noun	Adjective	Verb	Adverb
schoolmate	Yes	No	No	No
classmate	Yes	No	No	No

As nouns, schoolmate and classmate are synonyms defined as:

Other synonyms of schoolmate include class fellow, schoolfellow.

schoolmate (noun)	classmate (noun)
an acquaintance that you go to school with	an acquaintance that you go to school with