I mean, so's much of my extended family, that's how that works....

Anyway, did some reading, and it turns out we're both halfway there and it's surprisingly complicated (more so that "it's X not Y!")

So first is, gaelic, gaeilge, or gaelige? They're different words with different meanings and pronunciation, but broadly overlap depending on context.

Apparently it's a Scottish thing to refer to it as Gaelic and Irish Gaelic... And in Northern Ireland it's the other way around, it's geographical context.

Then you've got how if you're talking about both, it is okay to say Irish Gaelic and Scottish Gaelic, because you're usually on about how the languages relate to each other, but only if you're talking about the languages in English, because if you're talking about it in them then it's Gàidhlig or Gaeilge

Gaelic is a concept, which refers to it all (Scottish, Irish, adjective, noun) as one overarching thing, but then which variant word or hyphenated phrase is dependent on context and which you're actually talking about. And that's a social context.

And then there's apparently this thing with whether you're in one country or another (including Isle of Man) and that changes the word and context.

And then getting back to calling it "Irish", my family never said that, so it makes me wonder if it's a generational/regional thing as well, like bap/roll/bun in England.

Ah... Flipping heck!