A County is a territory of a country generally for administrative purposes. County comes from the French "conté" meaning jurisdiction of a count.
In the United States, a County is a political subdivision of a state, and its power of government and responsibilities varies widely from state to state, but usually rest in the "county seat" (a municipality), although sometimes could have several or no seats, and sometimes the county seat is just a big settlement.
So County responsibilities fluctuate, i.e. certain counties are governed by an elected body, which name might vary, as in "the county commission" or "county council", or "county court"; and in some states of Midwest, they exercise local powers, and across the United States certain counties might hold additional self-governing municipalities.
Thus the best answer would be (C): Counties' responsibilities can vary based on their locations.