migraine vs sick headache

migraine and sick headache both are nouns.

Word	Noun	Adjective	Verb	Adverb
migraine	Yes	No	No	No
sick headache	Yes	No	No	No

As nouns, migraine and sick headache are synonyms defined as:

migraine and sick headache: a severe recurring vascular headache; occurs more frequently in women than men

Other synonyms of migraine include hemicrania, megrim.

migraine (noun)	sick headache (noun)
a severe recurring vascular headache; occurs more frequently in women than men	a severe recurring vascular headache; occurs more frequently in women than men
	a headache accompanied by nausea