prime minister vs head of state

prime minister and head of state both are nouns.

Word	Noun	Adjective	Verb	Adverb
prime minister	Yes	No	No	No
head of state	Yes	No	No	No

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

prime minister: the person who is head of government (in several countries)
head of state: the chief public representative of a country who may also be the head of government

Other hypernyms of prime minister include chief of state.

prime minister (noun)	head of state (noun)
the person who is head of government (in several countries)	the chief public representative of a country who may also be the head of government