straighten out vs tidy

straighten out is not a noun while tidy is a noun.

Word	Noun	Adjective	Verb	Adverb
straighten out	No	No	Yes	No
tidy	Yes	Yes	Yes	No

As verbs, straighten out and tidy are synonyms defined as:

Other synonyms of straighten out include clean up, neaten, square away, straighten, tidy up.

straighten out (noun)	tidy (noun)
	receptacle that holds odds and ends (as sewing materials)

straighten out (adjective)	tidy (adjective)
	marked by order and cleanliness in appearance or habits
	large in amount or extent or degree
	(of hair) neat and tidy

straighten out (verb)	tidy (verb)
put (things or places) in order	put (things or places) in order
settle or put right
change for the better
make free from confusion or ambiguity; make clear
make straight
extricate from entanglement