body waste vs puke

body waste and puke both are nouns.

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

As nouns, puke is a hyponym of body waste; that is, puke is a word with a more specific, narrower meaning than body waste:

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

body waste (noun)	puke (noun)
waste matter (as urine or sweat but especially feces) discharged from the body	a person who is deemed to be despicable or contemptible
	the matter ejected in vomiting

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