peeve vs irritate

peeve is a noun but irritate is not a noun.

Word	Noun	Adjective	Verb	Adverb
peeve	Yes	No	Yes	No
irritate	No	No	Yes	No

As verbs, irritate is a hypernym of peeve; that is, irritate is a word with a broader meaning than peeve:

Other hypernyms of peeve include annoy, bother, chafe, devil, get at, get to, gravel, nark, nettle, rag, rile, vex.

peeve (noun)	irritate (noun)
an annoyed or irritated mood

peeve (verb)	irritate (verb)
cause to be annoyed, irritated, or resentful	excite to an abnormal condition, or chafe or inflame
	excite to some characteristic action or condition, such as motion, contraction, or nervous impulse, by the application of a stimulus
	cause annoyance in; disturb, especially by minor irritations