ache vs pain

ache and pain both are nouns.

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

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

Other hypernyms of ache include hurting.

ache (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

ache (verb)	pain (verb)
have a desire for something or someone who is not present	cause bodily suffering to and make sick or indisposed
be the source of pain	cause emotional anguish or make miserable
feel physical pain