The Santiago song and the Sweeney piece are almost certainly based on the same original melody, but that's not "Tha Mi Sgith" which is very different. The Sweeney piece is titled "Star of the County Down" which would appear to indicateindicates an Irish origin rather than a Scottish one. The Wikipedia page for "Star of the County Down" lists "Mädchen von Haithabu" as a recorded version.