head ache vs aching

head ache and aching both are nouns.

Word	Noun	Adjective	Verb	Adverb
head ache	Yes	No	No	No
aching	Yes	Yes	No	No

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

head ache: pain in the head caused by dilation of cerebral arteries or muscle contractions or a reaction to drugs
aching: a dull persistent (usually moderately intense) pain

Other hypernyms of head ache include ache.

head ache (noun)	aching (noun)
pain in the head caused by dilation of cerebral arteries or muscle contractions or a reaction to drugs	a dull persistent (usually moderately intense) pain

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