vomiting vs hematemesis

vomiting and hematemesis both are nouns.

Word	Noun	Adjective	Verb	Adverb
vomiting	Yes	No	No	No
hematemesis	Yes	No	No	No

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

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

Other hyponyms of vomiting include rumination, haematemesis, hyperemesis.

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