presidency vs administration

presidency and administration both are nouns.

Word	Noun	Adjective	Verb	Adverb
presidency	Yes	No	No	No
administration	Yes	No	No	No

As nouns, presidency and administration are synonyms defined as:

Other synonyms of presidency include presidential term.

presidency (noun)	administration (noun)
the office and function of president	a method of tending to or managing the affairs of some group of people (especially the group's business affairs)
the tenure of a president	the act of administering medication
	the act of meting out justice according to the law
	the act of governing; exercising authority
	the persons (or committees or departments etc.) who make up a body for the purpose of administering something
	the tenure of a president