megrim vs cephalalgia

megrim and cephalalgia both are nouns.

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

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

megrim: 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 megrim include head ache, headache.

megrim (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