vomit vs body waste

vomit and body waste both are nouns.

Word	Noun	Adjective	Verb	Adverb
vomit	Yes	No	Yes	No
body waste	Yes	No	No	No

As nouns, body waste is a hypernym of vomit; that is, body waste is a word with a broader meaning than vomit:

vomit: the matter ejected in vomiting
body waste: waste matter (as urine or sweat but especially feces) discharged from the body

Other hypernyms of vomit include excrement, excreta, excretion, excretory product.

vomit (noun)	body waste (noun)
the reflex act of ejecting the contents of the stomach through the mouth	waste matter (as urine or sweat but especially feces) discharged from the body
a medicine that induces nausea and vomiting
the matter ejected in vomiting

vomit (verb)	body waste (verb)
eject the contents of the stomach through the mouth