vomit vs excrement

vomit and excrement both are nouns.

Word	Noun	Adjective	Verb	Adverb
vomit	Yes	No	Yes	No
excrement	Yes	No	No	No

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

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

Other hypernyms of vomit include body waste, excreta, excretion, excretory product.

vomit (noun)	excrement (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)	excrement (verb)
eject the contents of the stomach through the mouth