Original: They were informally known as "West Germany" and "East Germany", and the two parts of Berlin as "West Berlin" and "East Berlin".
Simplified: The Kings of Prussia were also "German Emperors", but they did not call themselves "Emperors of Germany". However, Hitler started to abuse his power and declared himself "Führer" (leader). Many important people in history are thought of as "German", because they are at the heart of German culture, although they did not always live in Germany.