schoolwork vs school assignment

schoolwork and school assignment both are nouns.

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

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

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

Other synonyms of schoolwork include homework.

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