I understand the origin of the name Ginsburg as follows. It is German in origin, but a shortened/corruption of German. It has two elements. Burg means a citadel, or castle on a hill. Similar, but different from berg, which means hill. They may look similar, but are pronounced quite differently in German. Gins is more difficult. Some say it is a corruption of Gunz, and there is a town near a river Gunz called Gunzburg in Austria. But this is probably not the source of the name, but a different corruption. The source is probably Koenigs, which means King's. Thus the name means King's citadel, or King's castle on a hill.
Kinsborsky sounds Polisk. Sky means a citizen of, it indicates you come from somewhere, or someone. The rest just sounds like a Polishisation of a German name. Perhaps it was in someones interest to sound more Polish, at a certain time, and so adapted their name.