classmate vs schoolmate

classmate and schoolmate both are nouns.

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

As nouns, classmate and schoolmate are synonyms defined as:

Other synonyms of classmate include class fellow, schoolfellow.

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