aching vs pain

aching and pain both are nouns.

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

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

Other hypernyms of aching include hurting.

aching (noun)	pain (noun)
a dull persistent (usually moderately intense) pain	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

aching (adjective)	pain (adjective)
causing a dull and steady pain

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