written assignment vs writing assignment

written assignment and writing assignment both are nouns.

Word	Noun	Adjective	Verb	Adverb
written assignment	Yes	No	No	No
writing assignment	Yes	No	No	No

As nouns, written assignment and writing assignment are synonyms defined as:

written assignment and writing assignment: an assignment to write something

written assignment (noun)	writing assignment (noun)
an assignment to write something	an assignment to write something