As a hyphenated-American (very, very hyphenated), I find the term "Ulster-Scots" to be most convenient. I have several families who came to the American colonies from Ulster in the early 1700's; I refer to those connections as Ulster-Scots. My paternal grandfather was born in Scotland, and his family came to the U.S. in the late 1800's when he was five years old. That grandfather married a women whose parents were born in Ireland (Oh, the horror of it all; I've heard stories.), thus starting a Scotch-Irish (as I heard it called when I was young) line. In the end, it does not really matter what these groups are called, but it is convenient to have separate and easily understood terms for the two groups. I have never had to explain what I meant by Ulster-Scots, and I usually refer to the others as "Scotch & Irish" to preclude the need for a followup explanation.