president vs head of state

president and head of state both are nouns.

Word	Noun	Adjective	Verb	Adverb
president	Yes	No	No	No
head of state	Yes	No	No	No

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

president: the chief executive of a republic
head of state: the chief public representative of a country who may also be the head of government

Other hypernyms of president include chief of state.

president (noun)	head of state (noun)
the chief executive of a republic	the chief public representative of a country who may also be the head of government
an executive officer of a firm or corporation
the head administrative officer of a college or university
the officer who presides at the meetings of an organization