belief vs presence

belief and presence both are nouns.

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

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

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

belief (noun)	presence (noun)
any cognitive content held as true	the act of being present
a vague idea in which some confidence is placed	dignified manner or conduct
	the impression that something is present
	the immediate proximity of someone or something
	an invisible spiritual being felt to be nearby
	the state of being present; current existence