"A term in linguistics" is imprecise — it's also a term outside of linguistics. The phrase "term of art" means basically "I know that you think you know what this means based on the words, but it is a special defined term that means something particular in this field." It is generally used to correct someone who seems to be viewing a term of art as a common English phrase, so the precision is useful.
Seems like "idiomatic" already fits this perfectly. Is "term of art" in some way different? maybe has a more of a "you can't really understand it as an outsider," sense?:
Idiomatic:
A speech form or an expression of a given language that is peculiar to itself grammatically or cannot be understood from the individual meanings of its elements, as in keep tabs on.
A specialized vocabulary used by a group of people; jargon.
"Term of art" means that it has a technical meaning in a specific field, while "idiom" just means that a phrase has a meaning. For example, "a dime a dozen" is an idiom but not a term of art. If you wanted to avoid the phrase "term of art" for some reason, "idiom" would be a reasonable alternative.
"a technical meaning in a specific field" is one of the definitions of idiom (as given above)—they literally list 'jargon' as a synonym ("The specialized language of a trade, profession, or similar group, especially when viewed as difficult to understand by outsiders."). That entry was from: The American Heritage® Dictionary of the English Language, 5th Edition.
Since idiom has both the structural denotation of a phrase being semantically 'atomic' (you lose the meaning if you break it into pieces), plus its synonymity with 'jargon', there appears to be nothing added in "term of art".
—but maybe this is a lesser known meaning of 'idiom'.
To start, “idiomatic” is an adjective while “term of art” is a noun. The word “idiom” in the sense you are quoting refers to the whole language/dialect/way of speaking, not one word. The sense of “idiom” meaning one phrase (maybe shortened from “idiomatic expression” or something?) does not mean the same thing as “term of art”, but is more like a common expression in a particular language / dialect. It does not have the sense of a specific technical meaning for a word, distinct from the ordinary definition.
These words are not synonyms, and should not be substituted.
And there’s what I was looking for :) I did overlook that ‘idiom’ applies to a full language/dialect.
I think you’re overstating your case though when you say “It does not have the sense of a specific technical meaning for a word, distinct from the ordinary definition”—since jargon is a synonym for one sense of idiom and idiomatic is less specific in the group/individual distinction (and yes it’s an adjective but you can trivially employ it to construct an equivalent noun phrase so this matters little). That said my own case is clearly a stretch here lol.
Maybe more relevant is the fact one could just say “technical term” and they’d be understood perfectly—I’m pretty sure that phrase is the reason I’ve also never come across “term of art”.
A lot of things are jargon that are not terms of art. When I was practicing law, a lot of people in my legal circles would jokingly refer to their spouses as their "domestic associates". That's not a term of art, but it is lawyer's jargon or an idiomatic expression.
That’s an interesting example, though I read it as a kind of parody of jargon rather than actual jargon. It’s a tricky case though since jargon also has multiple senses and your classification fits one of them.
I’m curious whether you would consider “domestic partnership” to be both jargon and a term of art (I would).
It’s interesting reviewing definitions of ‘jargon’: while you do find things like e.g. “ specialized technical terminology characteristic of a particular subject” —mostly you find references to incoherent/nonsensical speech.
