politician vs mayor

politician and mayor both are nouns.

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

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

Other hyponyms of politician include governor, legislator, city manager.

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