What's distinguishes a chengyu (Chinese idiom) from a 4-character expression?
From

成语 versus 俗语 versus 谚语, what is the difference?


  成語 (idiom) include "situation description" , "common sense", and "words of wisdom". Mostly came from known historical references, like poems, classical literature or famous quotes by historic figures . 


4-character expressions are common phrases from unknown origin, just happen to have four characters, they are "idiomatic expressions" but they are not true idioms.