Difference between an enclave and an exclave

In political geography, an enclave is a territory whose geographical boundaries lie entirely within the boundaries of another territory.

An exclave, on the other hand, is a territory legally attached to another territory with which it is not physically contiguous.

Although the meanings of both words are close, an exclave may not necessarily be an enclave or vice versa. For example, Kaliningrad, an exclave of Russia, is not an enclave because it is surrounded not by one state, but by two: Lithuania and Poland; it also borders the Baltic Sea. On the other hand, Lesotho is an enclave in South Africa, but it is not politically attached to anything else, meaning that it is not an exclave.