malign vs besmirch

malign is an adjective but besmirch is not an adjective.

Word	Noun	Adjective	Verb	Adverb
malign	No	Yes	Yes	No
besmirch	No	No	Yes	No

As verbs, besmirch is a hypernym of malign; that is, besmirch is a word with a broader meaning than malign:

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

Other hypernyms of malign include asperse, calumniate, defame, denigrate, slander, smear, smirch, sully.

malign (adjective)	besmirch (adjective)
evil or harmful in nature or influence
having or exerting a malignant influence

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