If by some chance a spider does not despawn because you were near it for half a minecraft day, it turns from a monster spider into a wild spider. It lives under tall things like tree leaves or overhangs with cobwebs and will stay there during the day. They are no longer hostile unless you bother them, they'll evntually stop attacking you, and they will never despawn. Wild spiders a brown with purple eyes. They're like animals.
@cat, ohmygosh i wonder why!