emerge vs fall

emerge is not a noun while fall is a noun.

Word	Noun	Adjective	Verb	Adverb
emerge	No	No	Yes	No
fall	Yes	No	Yes	No

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

Other hyponyms of emerge include pop out, radiate, leak, escape, debouch, come out, fall out.

emerge (noun)	fall (noun)
	a sudden drop from an upright position
	the act of surrendering (usually under agreed conditions)
	a lapse into sin; a loss of innocence or of chastity
	a sudden sharp decrease in some quantity
	a free and rapid descent by the force of gravity
	a sudden decline in strength or number or importance
	when a wrestler's shoulders are forced to the mat
	a movement downward
	a downward slope or bend
	the season when the leaves fall from the trees
	the time of day immediately following sunset

emerge (verb)	fall (verb)
come out into view, as from concealment	occur at a specified time or place
become known or apparent	decrease in size, extent, or range
come out of	pass suddenly and passively into a state of body or mind
come up to the surface of or rise	be born, used chiefly of lambs
happen or occur as a result of something	come out; issue
	assume a disappointed or sad expression
	begin vigorously
	come as if by falling
	be cast down
	go as if by falling
	fall or flow in a certain way
	move downward and lower, but not necessarily all the way
	move in a specified direction
	descend in free fall under the influence of gravity
	slope downward
	drop oneself to a lower or less erect position
	lose an upright position suddenly
	to be given by assignment or distribution
	be captured
	fall to somebody by assignment or lot; passed
	come into the possession of
	to be given by right or inheritance
	be inherited by
	lose office or power
	yield to temptation or sin
	suffer defeat, failure, or ruin
	lose one's chastity
	die, as in battle or in a hunt
	be due
	come under, be classified or included
	touch or seem as if touching visually or audibly
	fall from clouds