badmouth vs defame

badmouth and defame both are verbs.

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

As verbs, defame is a hypernym of badmouth; that is, defame is a word with a broader meaning than badmouth:

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

Other hypernyms of badmouth include asperse, besmirch, calumniate, denigrate, slander, smear, smirch, sully.

badmouth (verb)	defame (verb)
speak unfavorably about	charge falsely or with malicious intent; attack the good name and reputation of someone