pain vs nuisance

pain and nuisance both are nouns.

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

As nouns, pain and nuisance are synonyms defined as:

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

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

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

pain: 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 pain include irritant, thorn, plague.

pain (noun)	nuisance (noun)
a somatic sensation of acute discomfort	(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
emotional distress; a fundamental feeling that people try to avoid
a symptom of some physical hurt or disorder

pain (verb)	nuisance (verb)
cause bodily suffering to and make sick or indisposed
cause emotional anguish or make miserable