head ache vs ache

head ache and ache both are nouns.

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

As nouns, ache is a hypernym of head ache; that is, ache 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
ache: a dull persistent (usually moderately intense) pain

Other hypernyms of head ache include aching.

head ache (noun)	ache (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 (verb)	ache (verb)
	have a desire for something or someone who is not present
	be the source of pain
	feel physical pain