public opinion vs belief

public opinion and belief both are nouns.

Word	Noun	Adjective	Verb	Adverb
public opinion	Yes	No	No	No
belief	Yes	No	No	No

As nouns, belief is a hypernym of public opinion; that is, belief is a word with a broader meaning than public opinion:

public opinion: a belief or sentiment shared by most people; the voice of the people
belief: any cognitive content held as true

public opinion (noun)	belief (noun)
a belief or sentiment shared by most people; the voice of the people	any cognitive content held as true
	a vague idea in which some confidence is placed