sinus headache vs head ache

sinus headache and head ache both are nouns.

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

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

sinus headache: a headache resulting from congestion or infection in the paranasal sinuses
head ache: pain in the head caused by dilation of cerebral arteries or muscle contractions or a reaction to drugs

Other hypernyms of sinus headache include cephalalgia, headache.

sinus headache (noun)	head ache (noun)
a headache resulting from congestion or infection in the paranasal sinuses	pain in the head caused by dilation of cerebral arteries or muscle contractions or a reaction to drugs