desperate criminal vs felon

desperate criminal and felon both are nouns.

Word	Noun	Adjective	Verb	Adverb
desperate criminal	Yes	No	No	No
felon	Yes	No	No	No

As nouns, felon is a hypernym of desperate criminal; that is, felon is a word with a broader meaning than desperate criminal:

desperate criminal: a bold outlaw (especially on the American frontier)
felon: someone who has committed a crime or has been legally convicted of a crime

Other hypernyms of desperate criminal include criminal, crook, malefactor, outlaw.

desperate criminal (noun)	felon (noun)
a bold outlaw (especially on the American frontier)	someone who has committed a crime or has been legally convicted of a crime
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