belief vs intuition

belief and intuition both are nouns.

Word	Noun	Adjective	Verb	Adverb
belief	Yes	No	No	No
intuition	Yes	No	No	No

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

Other hyponyms of belief include presence, effect, first blush, hunch, suspicion.

belief (noun)	intuition (noun)
any cognitive content held as true	instinctive knowing (without the use of rational processes)
a vague idea in which some confidence is placed	an impression that something might be the case