As I was told: Tysk = Teutons = Deutsch (which includes Dutch). The Teutons were the origin of the Teutonic Knights that settled in the northern lands after the First AD. Fascinating history. Hope this helps.
almost (and sorry to be the smartass here) it actually is derived from old high german diutisc or thiutisk which meant "of the people" and comes from old high german thiot "people" in contrast to "of the latins"