hemicrania vs head ache

hemicrania and head ache both are nouns.

Word	Noun	Adjective	Verb	Adverb
hemicrania	Yes	No	No	No
head ache	Yes	No	No	No

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

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

Other hypernyms of hemicrania include cephalalgia, headache.

hemicrania (noun)	head ache (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