co-ed vs coeducational

co-ed is a noun but coeducational is not a noun.

Word	Noun	Adjective	Verb	Adverb
co-ed	Yes	Yes	No	No
coeducational	No	Yes	No	No

As adjectives, co-ed and coeducational are synonyms defined as:

co-ed (noun)	coeducational (noun)
a female student at a coeducational college or university

co-ed (adjective)	coeducational (adjective)
attended by members of both sexes	attended by members of both sexes