homework vs school assignment

homework and school assignment both are nouns.

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

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

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

Other synonyms of homework include schoolwork.

homework (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