nuisance vs pain in the neck

nuisance and pain in the neck both are nouns.

Word	Noun	Adjective	Verb	Adverb
nuisance	Yes	No	No	No
pain in the neck	Yes	No	No	No

As nouns, pain in the neck is a hypernym of nuisance; that is, pain in the neck is a word with a broader meaning than nuisance:

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

Other hypernyms of nuisance include annoyance, bother, botheration, infliction, nuisance, pain, pain in the ass.

As nouns, nuisance and pain in the neck are synonyms defined as:

nuisance and pain in the neck: something or someone that causes trouble; a source of unhappiness

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

nuisance (noun)	pain in the neck (noun)
(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