straighten out vs neaten

straighten out and neaten both are verbs.

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

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

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

straighten out (verb)	neaten (verb)
put (things or places) in order	care for one's external appearance
settle or put right	put (things or places) in order
change for the better
make free from confusion or ambiguity; make clear
make straight
extricate from entanglement