sinus headache vs cephalalgia

sinus headache and cephalalgia both are nouns.

Word	Noun	Adjective	Verb	Adverb
sinus headache	Yes	No	No	No
cephalalgia	Yes	No	No	No

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

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

Other hypernyms of sinus headache include head ache, headache.

sinus headache (noun)	cephalalgia (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