writing assignment vs written assignment

writing assignment and written assignment both are nouns.

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

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

writing assignment and written assignment: an assignment to write something

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