cluster headache vs cephalalgia

cluster headache and cephalalgia both are nouns.

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

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

cluster headache: a painful recurring headache associated with the release of histamine from cells
cephalalgia: pain in the head caused by dilation of cerebral arteries or muscle contractions or a reaction to drugs

Other hypernyms of cluster headache include head ache, headache.

cluster headache (noun)	cephalalgia (noun)
a painful recurring headache associated with the release of histamine from cells	pain in the head caused by dilation of cerebral arteries or muscle contractions or a reaction to drugs