President vs chief of state

President and chief of state both are nouns.

Word	Noun	Adjective	Verb	Adverb
President	Yes	No	No	No
chief of state	Yes	No	No	No

As nouns, chief of state is a hypernym of President; that is, chief of state is a word with a broader meaning than President:

President: the person who holds the office of head of state of the United States government
chief of state: the chief public representative of a country who may also be the head of government

Other hypernyms of President include head of state.

President (noun)	chief of state (noun)
the office of the United States head of state	the chief public representative of a country who may also be the head of government
the person who holds the office of head of state of the United States government