mayor vs burgomaster

mayor and burgomaster both are nouns.

Word	Noun	Adjective	Verb	Adverb
mayor	Yes	No	No	No
burgomaster	Yes	No	No	No

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

mayor: the head of a city government
burgomaster: a mayor of a municipality in Germany or Holland or Flanders or Austria

Other hyponyms of mayor include ex-mayor, alcalde, mayoress.

mayor (noun)	burgomaster (noun)
the head of a city government	a mayor of a municipality in Germany or Holland or Flanders or Austria