Received wisdom in the past was that the Scottish song was the earlier, but the more I learn, the more I am inclined to doubt that. The tunes are not related, though Frank Kidson printed an English tune with a Scottish text set to it (Traditional Tunes, 1891, 24-26) which may have confused matters.

"Silly Sisters" recorded a slightly Anglicised arrangement of the set supplied by Robert Burns for the Scots Musical Museum; the SMM set is in the DT (see links above). "Dollar" (from thaler) was a well-known term for currency long before the USA was thought of, of course.