come through vs appear

come through and appear both are verbs.

Word	Noun	Adjective	Verb	Adverb
come through	No	No	Yes	No
appear	No	No	Yes	No

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

come through (verb)	appear (verb)
penetrate	come into sight or view
succeed in reaching a real or abstract destination after overcoming problems	be issued or published
attain success or reach a desired goal	come into being or existence, or appear on the scene
continue in existence after (an adversity, etc.)	appear as a character on stage or appear in a play, etc.
	give a certain impression of being something or having a certain aspect
	(of a proposition) seem to be true, probable, or apparent
	present oneself formally, as before a (judicial) authority