insult vs spite

insult and spite both are nouns.

Word	Noun	Adjective	Verb	Adverb
insult	Yes	No	Yes	No
spite	Yes	No	Yes	No

As verbs, spite is a hypernym of insult; that is, spite is a word with a broader meaning than insult:

Other hypernyms of insult include bruise, hurt, injure, offend, wound.

insult (noun)	spite (noun)
a deliberately offensive act or something producing the effect of deliberate disrespect	malevolence by virtue of being malicious or spiteful or nasty
a rude expression intended to offend or hurt	feeling a need to see others suffer

insult (verb)	spite (verb)
treat, mention, or speak to rudely	hurt the feelings of