Plenty of ordinary Scots may have thought of themselves as "Scotch" but the intelligentsia determined that "Scotch" -- apart from the whiskey -- was a barbarous anglicism to be avoided.
In the same way, it's not easy to say just what those Ulstermen or Northern Protestant Irishmen called themselves. "Ulster Scots" or "Ulstermen" or "Scots-Irish" were heard. Some may just have thought of themselves as Irish or British. "Scotch-Irish" is mostly an American term (later "corrected" to "Scots-Irish").
In the same way, it’s not easy to say just what those Ulstermen or Northern Protestant Irishmen called themselves. “Ulster Scots” or “Ulstermen” or “Scots-Irish” were heard. Some may just have thought of themselves as Irish or British. “Scotch-Irish” is mostly an American term (later “corrected” to “Scots-Irish”).
I know from research that both colonial and Canadian “Ulster Scots” gave “Irish” for their nationality in the census and other documents.
I have some, and I have done the research. “Scots-Irish” was an American invention, as I described, and as historians have written.
“Scots-Irish” was used to differentiate the 18th century Protestants, from the later, lower status “Irish” eg. 19th century Catholics.
The long settled “Irish” were effectively saying “we aren’t like these dirty, drunken, illiterate Irish newcomers. We are “Scots-Irish.”