This is something the present generation does not need to bother about.
But from the late 1940s to 1990, one had to remember that there were two countries making up Germany, and two distinct cities named Berlin.
The general practice in English media was to refer to West Germany and East Germany, and to West Berlin and East Berlin. But the Germans did not see it that way.
West Germany was formally called the Bundes Republik Deutschland (BRD) which translates to Federal Republic of Germany (FRG). This would appear on English documents produced by their government. The trains were marked DB (Deutsche Bundesbahn). The currency was the Deutsche Mark or DM, which was then one of the “good” hard currencies.
East Germany was formally called the Deutsche Demokratische Republik (DDR) which was similarly translated to German Democratic Republic (GDR). The trains were marked DR (Deutsche Reichsbahn) or German Government Railways. The currency was the Mark (M) which had little value outside the country. And let us not ask how democratic it was.
The city of Berlin was in the middle of East Germany. About 70% was the separate territory of West Berlin, for long an outpost of the “free world” in the middle of a Soviet-dominated country. East Berlin was the capital of the GDR, while the FRG had its capital in Bonn (a rather small city) safely located far from the East.
West Berlin reads the same as in English, as the words for West are the same:
This is a warning sign near the Berlin Wall:
“Warning! You are now leaving West Berlin”.
However, the “official” title for the other side is not Ost Berlin but merely Berlin, the capital of the GDR. This can be seen here:
Things became much simpler after 1990. One Germany, one capital, one Berlin, one currency.
The area in the former East Germany remains relatively less prosperous. But the people who lived there had the last laugh. One of their own, Angela Merkel, became one of the longest-lasting Chancellors of the united country.