presidency vs President

presidency and President both are nouns.

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

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

Other hyponyms of presidency include Chief Executive, President of the United States.

presidency (noun)	President (noun)
the office and function of president	the office of the United States head of state
the tenure of a president	the person who holds the office of head of state of the United States government