puking vs hyperemesis

puking and hyperemesis both are nouns.

Word	Noun	Adjective	Verb	Adverb
puking	Yes	No	No	No
hyperemesis	Yes	No	No	No

As nouns, hyperemesis is a hyponym of puking; that is, hyperemesis is a word with a more specific, narrower meaning than puking:

puking: the reflex act of ejecting the contents of the stomach through the mouth
hyperemesis: severe and excessive vomiting

Other hyponyms of puking include rumination, haematemesis, hematemesis.

puking (noun)	hyperemesis (noun)
the reflex act of ejecting the contents of the stomach through the mouth	severe and excessive vomiting