pop out vs come forth

pop out and come forth both are verbs.

Word	Noun	Adjective	Verb	Adverb
pop out	No	No	Yes	No
come forth	No	No	Yes	No

As verbs, come forth is a hypernym of pop out; that is, come forth is a word with a broader meaning than pop out:

Other hypernyms of pop out include come out, egress, emerge, go forth, issue.

pop out (verb)	come forth (verb)
come out suddenly or forcefully	come out of
exit briefly	happen or occur as a result of something
bulge outward
appear suddenly or unexpectedly; happen unexpectedly