rise vs come up

rise is a noun but come up is not a noun.

Word	Noun	Adjective	Verb	Adverb
rise	Yes	No	Yes	No
come up	No	No	Yes	No

As verbs, rise and come up are synonyms defined as:

Other synonyms of rise include arise, go up, lift, move up, uprise.

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

As verbs, rise and come up are synonyms defined as:

Other synonyms of rise include rise up, surface.

As verbs, rise and come up are synonyms defined as:

Other synonyms of rise include ascend, uprise.

As verbs, come up is a hypernym of rise; that is, come up is a word with a broader meaning than rise:

Other hypernyms of rise include arise, go up, lift, move up, rise, uprise.

rise (noun)	come up (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)	come up (verb)
return from the dead	result or issue
get up and out of bed	start running, functioning, or operating
increase in value or to a higher point	gather or bring together
become more extreme	gather (money or other resources) together over time
go up or advance	bring forth, usually something desirable
rise in rank or status	come up, of celestial bodies
exert oneself to meet a challenge	come to the surface
become heartened or elated	move toward, travel toward something or somebody or approach something or somebody
move upward	move upward
increase in volume	get something or somebody for a specific purpose
come to the surface	originate or come into being
rise to one's feet	be mentioned
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