There's something on the terminology on Wiki. It says the terms 'Scotch-Irish' and 'Scots-Irish' are used in the US to refer to certain groups of immigrants.

It also says:

Although referenced by Merriam-Webster dictionaries as having first appeared in 1744, the American term Scotch-Irish is undoubtedly older.

I know wiki doesn't always get things right, but for those interested in following up the thought it is a start.