phrasal idiom vs saying

phrasal idiom and saying both are nouns.

Word	Noun	Adjective	Verb	Adverb
phrasal idiom	Yes	No	No	No
saying	Yes	No	No	No

As nouns, saying is a hypernym of phrasal idiom; that is, saying is a word with a broader meaning than phrasal idiom:

phrasal idiom: an expression whose meanings cannot be inferred from the meanings of the words that make it up
saying: a word or phrase that particular people use in particular situations

Other hypernyms of phrasal idiom include expression, locution.

phrasal idiom (noun)	saying (noun)
an expression whose meanings cannot be inferred from the meanings of the words that make it up	a word or phrase that particular people use in particular situations