Currently, whether storage is enabled or not is keyed to cookies. Ideally we'd have separate prefs controlling each storage mechanism (cookies, storage, IndexedDB, cache), and they'd all be tied together in the UI with some kind of "disable all persistent storage" option. But people could override that by enabling (perhaps by UI, or just about:config) the various pieces. If we don't split all of them out, we should make it clearer (to both developers and end users) that some/all of them are unilaterally controlled by one pref.

We will update our communication around this permission to say "Site Data and Cookies" (in a dependency of bug 1421690) instead of offering separate permissions for the different storage options.