classwork vs school assignment

classwork and school assignment both are nouns.

Word	Noun	Adjective	Verb	Adverb
classwork	Yes	No	No	No
school assignment	Yes	No	No	No

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

classwork: the part of a student's work that is done in the classroom
school assignment: work, such as schoolwork or piecework, that is done at home

Other hypernyms of classwork include homework, schoolwork.

classwork (noun)	school assignment (noun)
the part of a student's work that is done in the classroom	work, such as schoolwork or piecework, that is done at home