OK, you have a point. But they all originally came from Ireland.
It started with the Irish Celts, who are from Ireland.
Some of those Irish Celts colonized Scotland in the first millenium (the Roman name for Ireland was Scotia) and grew distinct in culture.
Some of
them became the Scots-Irish, who were primarily Presbyterian Scot peasants, who were forced to move back to Ulster (Ireland) in the 17th and 18th Century to "Britishize it" but were still being oppressed by Sassanach tyranny and thus continued East, emigrating to North America.
Nobody made a distinction between Scots-Irish and "Irish" until the potato famine occured in the 1840's and the Catholic Irish joined the flood of emigrants. They were different in culture and regarded themselves as the "true" Irish where many Scots-Irish viewed them as Papist latecomers.
But anthropologists will tell you the predilictions for moodiness, drunkeness, violence and poetry is uniform across both groups.
