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The airport is located in Schönefeld, a municipality in Brandenburg, just outside of Berlin, which is also a state.

S-Bahn ring, usually called ring for short, refers to a prominent circular route around the city center of Berlin.

Federal in the American sense is a bit of a false friend for Germans: It means basically the same, but Americans use it to signify the unity of the states, while Germans talk about the states of the Union. So if we say federal borders we actually mean state borders and would otherwise say national or country borders.

Germany is federation of 16 or so states

Berlin is one of the 16 federal states of the Federal Republic of Germany.