Some of the comments above can give the mistaken impression that all of the Protestants in Ireland, or at least in Northern Ireland, are descended from the "planters" of the 17th and 18th centuries, and that they were all Scots Irish. In reality, many of the planters were English or Welsh, or even descended from French Huguenots. There was always a substantial native Irish Protestant population, as well. Moreover, after 300 years, the populations are so intermarried that there's no way to distinguish them.
When Henry VIII and Elizabeth I proclaimed the independence of the English church, not all Catholics in Ireland refused to go along. Some became Anglican by conviction; others changed religion for mercenary reasons; others were educated in Anglican schools (because the government supported those schools) and ended up feeling more comfortable as Protestants. Through the centuries, there were changes of religion in both directions, for all sorts of reasons, including intermarriage.
Some Americans think that if their families, descended from an ancestor in Ireland, were Protestant, they were really of Scots culture, not Irish. This is possibly true for the American immigrants who had been in Ireland for only a generation, or maybe even the second generation, especially if they had Scots surnames and were Presbyterian. Other than that it's a very misleading assertion, especially for later arrivals.
There are other misconceptions about the plantations. They were not all in Northern Ireland; there were numerous in the south. They didn't fill all of northern Ireland, but mostly the northern and eastern parts of the north. And they certainly didn't cause a mass migration of Catholics out of the northern counties, or of Protestants in the other direction. The two populations lived side by side for hundreds of years and mostly lived in relative peace, especially in the rural areas.
For well over 1000 years, there has been migration back and forth between Ireland and Scotland. For this reason, DNA analysis doesn't usually help to separate the two ethnicities.
My family were recent immigrants to the US from Northern Ireland; all four of my grandparents, as well as my father, were born there, in Counties Tyrone and Fermanagh. Although Protestant, they all considered themselves Irish, born into the Church of Ireland. One of my great-grandmothers had a surname (Griffin) thatcould be Welsh, so she was possibly of planter extraction, but she spoke Irish Gaelic. In the area where she was born, there are still many Griffins; some are Protestant and some are Catholic. Northern Ireland was a real melting pot.
Two of my grandparents have surnames that are probably native Irish; the others (Vaughan and Brown) are ambiguous. Many Irish people anglicized their surnames; for example,"Brehon" became "Brown", or "Cleary" became "Clark", or "Mahon" became "Vaughan". (This also happened in Scotland, making many surnames ambiguous.)
To sum it up, just as Italians or Germans who immigrated to the US in the 1800s were Americans within two generations, and intermarried with other nationalities, so Scots who emigrated to Ireland in the 1600s and then left for the US 100 years later, had by then absorbed much of the culture of Ireland, and intermarried with Irish neighbors.