mess up vs disorder

mess up is not a noun while disorder is a noun.

Word	Noun	Adjective	Verb	Adverb
mess up	No	No	Yes	No
disorder	Yes	No	Yes	No

As verbs, disorder is a hypernym of mess up; that is, disorder is a word with a broader meaning than mess up:

Other hypernyms of mess up include disarray.

mess up (noun)	disorder (noun)
	a disturbance of the peace or of public order
	a condition in which things are not in their expected places
	a physical condition in which there is a disturbance of normal functioning

mess up (verb)	disorder (verb)
make a mess of or create disorder in	bring disorder to
disturb the smoothness of	disturb in mind or make uneasy or cause to be worried or alarmed
make a mess of, destroy or ruin