'...The Lowland Scots, the Ulster Scots, and the Scotch-Irish of America are, as has been noted, one and the same race, but the two latter branches of the race have had experiences in Ulster and America which have strengthened their character and toughened their native fibre by the very difficulties they have been compelled to overcome... the Ulster Scot in his new environment ceased to be a Lowlander, though the seedbed of his race was the Lowlands of Scotland... he will make one more migration - this time to the New World, where freedom abounds and opportunity beckons. Here, amid new surroundings, he will undergo a further change, and here he will go his farthest lengths and attain his greatest heights. No longer a Lowland Scot or and Ulster Scot, he becomes the Scotch-Irishman of America - still of the same race as the Lowlander and the Ulster Scot, to be sure, but different from either by reason of his adjustment to a changed environment...'
from The Scotch-Irish of Colonial Pennsylvania by Wayland F Dunaway (University of North Carolina Press, 1944) p 26-27
Visit Ulster, Pennsylvania here.