school assignment vs schoolwork

school assignment and schoolwork both are nouns.

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

As nouns, school assignment and schoolwork are synonyms defined as:

school assignment and schoolwork: work, such as schoolwork or piecework, that is done at home

Other synonyms of school assignment include homework.

school assignment (noun)	schoolwork (noun)
work, such as schoolwork or piecework, that is done at home	work, such as schoolwork or piecework, that is done at home