annoyance vs nuisance

annoyance and nuisance both are nouns.

Word	Noun	Adjective	Verb	Adverb
annoyance	Yes	No	No	No
nuisance	Yes	No	No	No

As nouns, annoyance and nuisance are synonyms defined as:

annoyance and nuisance: something or someone that causes trouble; a source of unhappiness

Other synonyms of annoyance include bother, botheration, infliction, pain, pain in the ass, pain in the neck.

As nouns, nuisance is a hyponym of annoyance; that is, nuisance is a word with a more specific, narrower meaning than annoyance:

annoyance: something or someone that causes trouble; a source of unhappiness
nuisance: (law) a broad legal concept including anything that disturbs the reasonable use of your property or endangers life and health or is offensive

Other hyponyms of annoyance include irritant, thorn, plague.

annoyance (noun)	nuisance (noun)
the act of troubling or annoying someone	(law) a broad legal concept including anything that disturbs the reasonable use of your property or endangers life and health or is offensive
something or someone that causes trouble; a source of unhappiness	something or someone that causes trouble; a source of unhappiness
anger produced by some annoying irritation
an unpleasant person who is annoying or exasperating
the psychological state of being irritated or annoyed