hyperemesis vs puking

hyperemesis and puking both are nouns.

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

As nouns, puking is a hypernym of hyperemesis; that is, puking is a word with a broader meaning than hyperemesis:

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

Other hypernyms of hyperemesis include disgorgement, emesis, regurgitation, vomit, vomiting.

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