disbelieve vs distrust

disbelieve is not a noun while distrust is a noun.

Word	Noun	Adjective	Verb	Adverb
disbelieve	No	No	Yes	No
distrust	Yes	No	Yes	No

As verbs, distrust is a hyponym of disbelieve; that is, distrust is a word with a more specific, narrower meaning than disbelieve:

disbelieve: reject as false; refuse to accept
distrust: regard as untrustworthy; regard with suspicion; have no faith or confidence in

Other hyponyms of disbelieve include doubt, mistrust, suspect.

disbelieve (noun)	distrust (noun)
	the trait of not trusting others
	doubt about someone's honesty

disbelieve (verb)	distrust (verb)
reject as false; refuse to accept	regard as untrustworthy; regard with suspicion; have no faith or confidence in