1. adjective
a) Of, from, or pertaining to present-day Hungary, the ethnic Hungarian people or the Hungarian language.
b) Of, from, or pertaining to the Kingdom of Hungary, during the days of the Austro-Hungarian Empire, regardless of ethnicity.
2. noun
a) A person from present-day Hungary or of ethnic Hungarian descent.
The qualifier is the descriptive part of the name that would probably make up the entire name if you werent using Hungarian.
b) A person from the former Kingdom of Hungary, during the Austro-Hungarian Empire, regardless of that persons ethnicity.
Wikipedia foundation.