In both cases only a small fraction of their DNA is from the PIE (Proto-Indo-European) people.
But the PIE-descended people dominated the region, and their language came to be spoken by everyone.
This happened in most of Europe, Persia, and India. (In Ireland's case, Germanic English, with much vocabulary from Latin and French, replaced Celtic Goidelic - but all of them are branches on the PIE family tree.) And then Western Europe spread the PIE languages to the New World.
In both cases only a small fraction of their DNA is from the PIE (Proto-Indo-European) people.
But the PIE-descended people dominated the region, and their language came to be spoken by everyone.
This happened in most of Europe, Persia, and India. (In Ireland's case, Germanic English, with much vocabulary from Latin and French, replaced Celtic Goidelic - but all of them are branches on the PIE family tree.) And then Western Europe spread the PIE languages to the New World.
https://en.wikipedia.org/wiki/Indo-European_languages