belief vs feeling

belief and feeling both are nouns.

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

As nouns, belief and feeling are synonyms defined as:

Other synonyms of belief include impression, notion, opinion.

belief (noun)	feeling (noun)
any cognitive content held as true	the experiencing of affective and emotional states
a vague idea in which some confidence is placed	an intuitive understanding of something
	a physical sensation that you experience
	the sensation produced by pressure receptors in the skin
	a vague idea in which some confidence is placed
	the general atmosphere of a place or situation and the effect that it has on people