harass vs annoy

harass and annoy both are verbs.

Word	Noun	Adjective	Verb	Adverb
harass	No	No	Yes	No
annoy	No	No	Yes	No

As verbs, annoy is a hypernym of harass; that is, annoy is a word with a broader meaning than harass:

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

harass (verb)	annoy (verb)
exhaust by attacking repeatedly	cause annoyance in; disturb, especially by minor irritations
annoy continually or chronically