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.
These words are not synonyms, and should not be substituted.