haematemesis vs puking

haematemesis and puking both are nouns.

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

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

haematemesis: vomiting blood
puking: the reflex act of ejecting the contents of the stomach through the mouth

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

haematemesis (noun)	puking (noun)
vomiting blood	the reflex act of ejecting the contents of the stomach through the mouth