The term "Ulster Scots" came into being to replace, "Scotch-Irish," a term which, upon looking at it, would lead one to believe it applied to Irish who enjoyed drinking scotch whiskey.
It's commonly used in the United States to describe those people who immigrated to the US from Northern Ireland and settled mainly in the Appalachian and Piedmont regions from Pennsylvania through Georgia.
Though they are lumped together en masse and given a name seemingly descriptive of their origins, they weren't all Scots or Irish; some were English.
The Plantations of William and Mary moved families from England from the South all the way up through the North of Scotland into the Highlands. The Great Clearings left many Scots without their family lands, and they had no place to go.
The people were, however, predominantly from the Borderlands and Scottish Lowlands, and were an amalgamation of Pict, Brythonic Celts, Gaelic Celts, Scandinavians, Anglo-Saxons, and Normans.
The native Irish, and those who migrated to what would become Scotland, were almost certainly the same Celts who settled in Brittain. Different influences over time are probably responsible for the later differences in language and custom, many of which were probably from the people who already inhabited the lands where the Celts settled.
Irish Mythology mentions two races living in Ireland before the Gaels; the Tuatha de Danaan, and the Fomorians, and though these are obviously fanciful creations, it suggests the neothilic culture there was still extant when the Irish arrived..
By the way, "Spain" does appear in the Irish Mythological cycles, but it is more akin to heaven than a previous home.
Some would argue that the Normans were Scandinavian, but only early on. They intermarried with the native Franks and Gaels for a century before any of their number migrated to Scotland.
The people of the Plantations were also in Ireland for a while before they came here, so there was intermarriage there too. They were predominantly protestant, though some were Anglican and Catholic, and Presbyterianism was the major religion practiced in the region. But there are buts.
Researching my own family back to Ulster, I've run across some who were Catholic, and some who were Presbyterian. Most were Orangemen, but at least one was hanged for treason against the crown.
The violence which has lasted for centuries makes researching there difficult, as many churches and records were burned.