First, Kaliningrad is a city. Kaliningrad Oblast describes the territory in question. Second, Kaliningrad Oblast is not an enclave but rather a semi-exclave. Enclaves are wholly surrounded by a single territory (as Vatican City State is by Italy). Exclaves are wholly separated from the main part of the state to which they belong and may be bordered by any number of territories (in this case, Poland and Lithuania).
We must use semi-exclave here, however, because part of Kaliningrad Oblast is surrounded not by foreign territory but by a coastline contiguous with international waters.
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