German vs East German

German and East German both are nouns.

Word	Noun	Adjective	Verb	Adverb
German	Yes	Yes	No	No
East German	Yes	Yes	No	No

As nouns, East German is a hyponym of German; that is, East German is a word with a more specific, narrower meaning than German:

Other hyponyms of German include Teuton, Boche, Hun, Jerry, Kraut, Krauthead, Berliner, Prussian, Bavarian.

German (noun)	East German (noun)
the standard German language; developed historically from West Germanic	a native or inhabitant of the former republic of East Germany
a person of German nationality

German (adjective)	East German (adjective)
of or pertaining to or characteristic of Germany or its people or language	relating to or characteristic of East Germany