smirch vs badmouth

smirch is a noun but badmouth is not a noun.

Word	Noun	Adjective	Verb	Adverb
smirch	Yes	No	Yes	No
badmouth	No	No	Yes	No

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

smirch: charge falsely or with malicious intent; attack the good name and reputation of someone
badmouth: speak unfavorably about

Other hyponyms of smirch include assassinate, libel, drag through the mud, malign, traduce.

smirch (noun)	badmouth (noun)
an act that brings discredit to the person who does it
a blemish made by dirt

smirch (verb)	badmouth (verb)
charge falsely or with malicious intent; attack the good name and reputation of someone	speak unfavorably about
smear so as to make dirty or stained