It's interesting that unmodified "Gaelic" apparently refers to Scots Gaelic in Wales. If you asked me about "Gaelic", I'd assume you meant Irish Gaelic.
Online people can get a bit snippy about calling it the wrong thing, even though they don't necessarily have a great grasp of the language itself. There's a lot of post-colonial baggage with regard to people's relationship with the language (IMO)
In Ireland, the term Gaelic typically refers to the general Irish identity and culture. Almost always, when people use the term Gaelic in everyday speech they're referring to Gaelic Games, which are the indigenous sports of Ireland. Gaelic Football, Hurling, Handball, and rounders. The GAA ( Gaelic Athletic Association ) that governs the games are in every village, town, and city, and the sports are probably the strongest expression of Gaelic culture in the country.
Some highlights of the 2 most popular games.
Gaelic Football https://www.youtube.com/watch?v=FT5Zjx4fTXI
Could it have been some lost continental Germanic/Celtic tribe? Seems less likely on balance. Maybe a big discovery still to come that will clear it up. A tomb somewhere under a housing estate in Glasgow or something.
Unless you know better, or of some reform, in which case I defer!
I'm from the United States.
(While we're here, we might also note that the term "Erse", referring to Scots Gaelic, is in fact the word "Irish".)