come to mind vs appear

come to mind and appear both are verbs.

Word	Noun	Adjective	Verb	Adverb
come to mind	No	No	Yes	No
appear	No	No	Yes	No

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

come to mind (verb)	appear (verb)
be remembered	come into sight or view
	be issued or published
	come into being or existence, or appear on the scene
	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