Since West Germany considered East Germany to be occupied territory, East Germans had automatic citizenship in the west. This made it uniquely easy to emigrate into the much wealthier country.
For the East there were 2 citizenships. They had no adjectives, they only talked about "citizen of the German Democratic Republic" and "citizen of the Federal Republic of Germany".
The occupation view was not official politics after 1970. The West had recognized the East as a state. But citizens of both states were assumed to have the same citizenship.
Edit: recognized as state should maybe recognized as some kind of state. Like the citizenship there were numerous differences compared to other foreign nation states.