It's even more complicated. Ireland has experienced one wave of viking and two waves of english settlers. The vikings settled around Dublin in the 9th and 10th century, until they were beaten by Brian Buro in the Battle of Clontarf. Then after the normannic conquest of England, the Normans set also out to conquer Ireland in the 11th and 12th century, and the King of England became Lord of Ireland, and normannic and english earls were ruling Ireland. But with time, the english control of Ireland lapsed, as the Kings of England were occupied with their territories in France and the battles in the Hundred Years War. The english earls became more and more irish, started to wear irish clothes, intermarried with irish aristocrats and even started to talk Irish Gaelic.
But after the loss of the Hundred Years War and all their continental territory, the english kings started to look into Ireland, especially Henry VIII and Elizabeth I. They managed to revive english rule in Ireland, and they started to send settlers from England, Wales and Scotland to Ireland. Those were the New English, compared with the Old English who came 400 years earlier. Most North Irish Protestants are the descendants of those settlers.