molest vs annoy

molest and annoy both are verbs.

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

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

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

molest (verb)	annoy (verb)
annoy continually or chronically	cause annoyance in; disturb, especially by minor irritations
harass or assault sexually; make indecent advances to