idiomatic expression vs set phrase

idiomatic expression and set phrase both are nouns.

Word	Noun	Adjective	Verb	Adverb
idiomatic expression	Yes	No	No	No
set phrase	Yes	No	No	No

As nouns, idiomatic expression and set phrase are synonyms defined as:

idiomatic expression and set phrase: an expression whose meanings cannot be inferred from the meanings of the words that make it up

Other synonyms of idiomatic expression include idiom, phrasal idiom, phrase.

idiomatic expression (noun)	set phrase (noun)
an expression whose meanings cannot be inferred from the meanings of the words that make it up	an expression whose meanings cannot be inferred from the meanings of the words that make it up