hemicrania vs cephalalgia

hemicrania and cephalalgia both are nouns.

Word	Noun	Adjective	Verb	Adverb
hemicrania	Yes	No	No	No
cephalalgia	Yes	No	No	No

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

hemicrania: a severe recurring vascular headache; occurs more frequently in women than men
cephalalgia: pain in the head caused by dilation of cerebral arteries or muscle contractions or a reaction to drugs

Other hypernyms of hemicrania include head ache, headache.

hemicrania (noun)	cephalalgia (noun)
a severe recurring vascular headache; occurs more frequently in women than men	pain in the head caused by dilation of cerebral arteries or muscle contractions or a reaction to drugs