appear vs occur

appear and occur both are verbs.

Word	Noun	Adjective	Verb	Adverb
appear	No	No	Yes	No
occur	No	No	Yes	No

As verbs, occur is a hyponym of appear; that is, occur is a word with a more specific, narrower meaning than appear:

Other hyponyms of appear include gleam, fulminate.

appear (verb)	occur (verb)
come into sight or view	come to pass
be issued or published	come to one's mind; suggest itself
come into being or existence, or appear on the scene	to be found to exist
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