C is B's exclave, but is not an enclave.

C is B's exclave, and A's enclave.

An exclave is strip of land that belongs to an entity (like a country or a region) but that is not connected to it by land (islands are not counted). The strip of land is surrounded by other political entities. A good example is Kaliningrad Oblast (the region around the Russian city Kaliningrad). It belongs to the Russian Federation, but is separated from the rest of that country by territory belonging to Lithuania and Poland.