To cut to the chase, an enclave is a bit of a foreign country inside your country, and an exclave is a bit of your country inside a foreign country; it all depends on from whose side you are looking at it, just as I am an immigrant in Australia and an emigrant in Germany (although these days I like to think of myself as an Australian who was born in the wrong country).
Oh, and before I forget: all enclaves are also exclaves, but not all exclaves are enclaves. An exclave that is surrounded by two countries (one on each side) isn't an enclave, as an enclave has to be surrounded by a single country. I just thought you would also want to know that.
A:
possesses 5 exclaves (A1, A2, A3, A4, and A5): it is impossible to go from the main part of A to any of these parts going only through territory of A; however:
A1 and A2 are not enclaves: neither of them is surrounded by a single "foreign" territory;
A1 is a semi-enclave and a semi-exclave: it has an unsurrounded sea border;
A2 is an exclave of A: it is separated from A;
A3 is an enclave: it is completely surrounded by B;
A4 and A5 are counter-enclaves (also known as second-order enclaves): territories belonging to A that are encroached inside the enclave E;
contains 1 enclave (E): "foreign" territory totally surrounded by territory of A;
contains 1 counter-counter-enclave, or third-order enclave (E1).
B:
contains 2 enclaves (A3 and D).
C:
continuous territory, contains no enclave or exclave
D:
is an enclaved territory: it is territorially continuous, but its territory is totally surrounded by a single "foreign" territory (B).
E:
is an enclaved territory: it is inside A;
contains 2 enclaves (A4 and A5), which are counter-enclaves of A;
possesses 1 counter-enclave (E1), which is a counter-counter-enclave as viewed by A and contained within A5.
"What brought all this on?" and "How will that put food on my table?" I hear you ask. It won't, but it'll make your hair stand up - if you have any left to speak of - should you follow the examples in the above diapgram.
The whole thing reared its ugly head when a German friend from my hometown in Braunschweig emailed me the above video clip of an exclave my (c)old hometown used to have near the city of Bremen. The whole thing dates back to the time when Germany was still a wet dream in someone's mind and the place was just an assortment of twenty-six territories, most ruled by royal families, and included four kingdoms, six grand duchies, five duchies (six before 1876), seven principalities, three free Hanseatic cities, and one imperial territory. This particular leftover from that patchwork of territories was not ironed out until 1972 [click].
Since you have been a long-time reader of this blog, by sheer osmosis you ought to be fluent in German by now, but if you're not, you can skip the first YouTube video and click on the one immediately above which explains an even crazier situation which to this day exists in Belgium and the Netherlands, with borders zigzagging through streets, houses, and even bedrooms, which makes knowing which side of the bed you were conceived on almost as important as knowing who your father was.
Sitting here on the verandah, screened from the lane by almost an acre of "front garden" and my back protected by another six acres, and the whole lot surrounded by the Clyde River, I like to think of "Riverbend" as counter-enclave A5 with E being the mighty river and E1 being my pond.