Both East Germany (when it existed) and West Germany were "Germany" and at least theoretically belived their government was the legitimate one for the whole territory, but products made in both were generally distinguished on their labels.
In the 60's and early 70's the GDR dropped this idea and worked towards being recognized as its own souvereign state, and insisted that there are two German states (the GDR and the FRG).
This eventually resulted in the "Basic Treaty" from 1972, and the GDR joining the UNO in 1973 (see: https://en.wikipedia.org/wiki/Basic_Treaty,_1972, or the much more detailed entry in the German Wikipedia: https://de.wikipedia.org/wiki/Grundlagenvertrag)