exist vs come

exist is not a noun while come is a noun.

Word	Noun	Adjective	Verb	Adverb
exist	No	No	Yes	No
come	Yes	No	Yes	No

As verbs, come is a hyponym of exist; that is, come is a word with a more specific, narrower meaning than exist:

exist (noun)	come (noun)
	the thick white fluid containing spermatozoa that is ejaculated by the male genital tract

exist (verb)	come (verb)
have an existence, be extant	come to pass; arrive, as in due course
support oneself	be found or available
	reach or enter a state, relation, condition, use, or position
	happen as a result
	have a certain priority
	come to one's mind; suggest itself
	move toward, travel toward something or somebody or approach something or somebody
	be received
	cover a certain distance
	reach a destination; arrive by movement or progress
	experience orgasm
	come under, be classified or included
	proceed or get along
	extend or reach
	to be the product or result
	exist or occur in a certain point in a series
	be a native of
	to measure up to in kind or quality
	add up in number or quantity
	come forth
	come from; be connected by a relationship of blood, for example