come back vs catch up

come back and catch up both are verbs.

Word	Noun	Adjective	Verb	Adverb
come back	No	No	Yes	No
catch up	No	No	Yes	No

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

come back (verb)	catch up (verb)
be restored	learn belatedly; find out about something after it happened
go back to something earlier	reach the point where one should be after a delay
answer back
even the score, in sports