chest pain vs pain

chest pain and pain both are nouns.

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

As nouns, pain is a hypernym of chest pain; that is, pain is a word with a broader meaning than chest pain:

Other hypernyms of chest pain include hurting.

chest pain (noun)	pain (noun)
pain in the chest	a somatic sensation of acute discomfort
	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

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