public office vs office

public office and office both are nouns.

Word	Noun	Adjective	Verb	Adverb
public office	Yes	No	No	No
office	Yes	No	No	No

As nouns, office is a hypernym of public office; that is, office is a word with a broader meaning than public office:

Other hypernyms of public office include berth, place, position, post, situation.

public office (noun)	office (noun)
a position concerning the people as a whole	a religious rite or service prescribed by ecclesiastical authorities
	the actions and activities assigned to or required or expected of a person or group
	a job in an organization
	place of business where professional or clerical duties are performed
	professional or clerical workers in an office
	an administrative unit of government
	(of a government or government official) holding an office means being in power