Apparently this has been discussed already 4 years ago. We have three tags
idioms
Questions about those phrases with fixed words used as a single unit, which typically have a meaning beyond what is...expression
A set phrase used commonly in the Japanese languageset-phrases
Phrases with fixed words used as a single unit, many of which are idioms.(emphasis mine)
I think we should make expression a synonym of set-phrases (or the other way around), but I think for tags about set phrases, expressions, idioms, we have at least one too many.
(For inspiration, the difference between the words "phrase, expression, idiom" has been asked over on English.SE.)