A number of the obituaries for the American author Jerome D Salinger, who died on Thursday, reported that he was the son of a Scots-Irish or Scotch-Irish mother and a Jewish businessman father. I was interested in the suggestion that his mother might have been Scotch-Irish and have Ulster-Scots roots but on reading a little further it seems that his mother Marie (or Miriam) Jillich was actually of mixed Scottish and Irish descent.
That is one of the difficulties with the terms Scotch-Irish and Scots-Irish, but especially the newer term Scots-Irish. It is often assumed to mean 'partly Scottish and partly Irish'. Some newspapers described Marie more accurately as Scottish-Irish, Scottish/Irish, half-Scottish and half-Irish, or of mixed Scottish-Irish descent, but the most common description was Scots-Irish.
Some modern writers prefer the term Scots-Irish but I prefer the traditional term Scotch-Irish, which has a long history, which is still used more frequently and which is therefore less open to misunderstanding. It refers not to a mixed Scottish and Irish ancestry but to the descendants of the Ulster-Scots who emigrated from Ulster to America.