burst vs erupt

burst is a noun but erupt is not a noun.

Word	Noun	Adjective	Verb	Adverb
burst	Yes	No	Yes	No
erupt	No	No	Yes	No

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

Other hyponyms of burst include crump, go off, belch, extravasate.

As verbs, burst and erupt are synonyms defined as:

burst and erupt: force out or release suddenly and often violently something pent up

Other synonyms of burst include break.

burst (noun)	erupt (noun)
the act of exploding or bursting
rapid simultaneous discharge of firearms
a sudden flurry of activity (often for no obvious reason)
a sudden intense happening

burst (verb)	erupt (verb)
come open suddenly and violently, as if from internal pressure	become active and spew forth lava and rocks
break open or apart suddenly and forcefully	start abruptly
emerge suddenly	erupt or intensify suddenly
burst outward, usually with noise	become raw or open
force out or release suddenly and often violently something pent up	break out
move suddenly, energetically, or violently	appear on the skin
cause to burst	force out or release suddenly and often violently something pent up
be in a state of movement or action	start to burn or burst into flames