headache vs aching

headache and aching both are nouns.

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

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

headache: 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 headache include ache.

headache (noun)	aching (noun)
something or someone that causes anxiety; a source of unhappiness	a dull persistent (usually moderately intense) pain
pain in the head caused by dilation of cerebral arteries or muscle contractions or a reaction to drugs

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