written agreement vs agreement

written agreement and agreement both are nouns.

Word	Noun	Adjective	Verb	Adverb
written agreement	Yes	No	No	No
agreement	Yes	No	No	No

As nouns, agreement is a hypernym of written agreement; that is, agreement is a word with a broader meaning than written agreement:

written agreement: a legal document summarizing the agreement between parties
agreement: the statement (oral or written) of an exchange of promises

Other hypernyms of written agreement include instrument, legal document, legal instrument, official document, understanding.

written agreement (noun)	agreement (noun)
a legal document summarizing the agreement between parties	compatibility of observations
	the thing arranged or agreed to
	the verbal act of agreeing
	the statement (oral or written) of an exchange of promises
	the determination of grammatical inflection on the basis of word relations
	harmony of people's opinions or actions or characters