emerge vs pop out

emerge and pop out both are verbs.

Word	Noun	Adjective	Verb	Adverb
emerge	No	No	Yes	No
pop out	No	No	Yes	No

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

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

emerge (verb)	pop out (verb)
come out into view, as from concealment	come out suddenly or forcefully
become known or apparent	exit briefly
come out of	bulge outward
come up to the surface of or rise	appear suddenly or unexpectedly; happen unexpectedly
happen or occur as a result of something