"I find Scotch and Scots equivalent in this context. Scots is not a drink, though."

Depends where you are! The term "Scotch" was seemingly originally an English term which came into use in Scotland too at a certain date often replacing the home terms of Scots or Scottish (there are various older spellings of these terms like Scottis). At some point, I suspect maybe in the early to mid 20thC, in the wake of the Scottish Literary Renaissance the term Scotch started to fall out of use in Scotland itself and the home grown terms Scots and Scottish reasserted themselves. So in Scotland for the most part the term "Scotch" became more restricted to a descriptive term for certain things like Scotch whisky, Scotch mist, Scotch eggs etc etc. Whereas when talking about themselves or their country Scottish people tend to prefer the terms Scots or Scottish. That change in usage didn't happen so much in the diaspora hence the word Scotch is more common with them when talking about people. But if you call a Scottish person "Scotch" there is a fair chance that they will correct you. They are not likely to be offended but will commonly say "no I am Scottish or Scots" So they are not equivalent terms in Scotland itself.

The term "Scotch Irish" AFAIK tends to be a North American term for the Scottish emigrants who first travelled to Ireland as part of the Ulster Plantation then at some point moved on from there across the Atlantic. This side of the Atlantic both in Scotland and in Ireland itself the descendents of this community tend to be called "Ulster Scots" rather than "Scotch Irish".