disbelieve vs mistrust

disbelieve is not a noun while mistrust is a noun.

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

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

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

Other hyponyms of disbelieve include doubt, distrust, suspect.

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

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