Luxemburger vs European

Luxemburger and European both are nouns.

Word	Noun	Adjective	Verb	Adverb
Luxemburger	Yes	Yes	No	No
European	Yes	Yes	No	No

As nouns, European is a hypernym of Luxemburger; that is, European is a word with a broader meaning than Luxemburger:

Luxemburger (noun)	European (noun)
a native or inhabitant of Luxembourg	a native or inhabitant of Europe

Luxemburger (adjective)	European (adjective)
of or relating to or characteristic of the grand duchy of Luxemburg or its people	of or relating to or characteristic of Europe or the people of Europe
of or relating to the capital city of Luxemburg