mayor vs politician

mayor and politician both are nouns.

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

As nouns, politician is a hypernym of mayor; that is, politician is a word with a broader meaning than mayor:

Other hypernyms of mayor include civil authority, civil officer.

mayor (noun)	politician (noun)
the head of a city government	a person active in party politics
	a leader engaged in civil administration
	a schemer who tries to gain advantage in an organization in sly or underhanded ways