rise vs emerge

rise is a noun but emerge is not a noun.

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

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

Other hyponyms of rise include resurface, bubble up, intumesce, swell, well.

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

Other hyponyms of rise include resurge, come forth, come, follow, swell, well up, head.

rise (noun)	emerge (noun)
the act of changing location in an upward direction
increase in price or value
the property possessed by a slope or surface that rises
the amount a salary is increased
an increase in cost
a growth in strength or number or importance
a wave that lifts the surface of the water or ground
a movement upward; rise above the ground
(theology) the origination of the Holy Spirit at Pentecost
an upward slope or grade (as in a road)

rise (verb)	emerge (verb)
return from the dead	come out into view, as from concealment
get up and out of bed	become known or apparent
increase in value or to a higher point	come out of
become more extreme	come up to the surface of or rise
go up or advance	happen or occur as a result of something
rise in rank or status
exert oneself to meet a challenge
become heartened or elated
move upward
increase in volume
come to the surface
rise to one's feet
move to a better position in life or to a better job
come up, of celestial bodies
take part in a rebellion; renounce a former allegiance
rise up
come into existence; take on form or shape