It is occasionally desirable that some content be restricted in terms of who can read it, and who can upload to it. To accomplish this, the internal database is divided into two: the Open database and the Local database. Each one is divided again in two, into "wide use" and "narrow use".
Translations here are available to all the users of the service.
At this time there's not much difference between Anonymous and Public other than the requirement for an account to access Public resources.
Translations uploaded with anonymous visibility can be retrieved by anyone, whether or not they have an account on the service. This is the appropriate place to put translations that can't, won't or don't need to use authentication.
Translations uploaded with public visibility can be retrieved by anyone who has an account on the service, whether or not you've created them as SubOrdinate users.
Every SuperOrdinate user has his own 'Local' database. In this manner, SuperOrdinate Alice trying to access translations only for SuperOrdinate Bob would fail: while she may have the right link, it points to a location within her own Local database rather than Bob's.
Uploading to Private denies the wider community use of those translations, and so significant use of it (at the moment, defined as 'having more than 16 SubOrdinate users') is something that will cost, whereas the other three visibilities are free.
Translations uploaded with private visibility can only be retrieved by those sharing that local database, as well as the uploader. The effect here is to restrict acess to SubOrdinate users you've created. Private is the appropriate visibility for uploading content you may wish to moderate.
Translations uploaded with personal visiblity can only be retrieved by the user who uploaded them. Think it would be funny to have "File-Then-Exit-label" say "Exeunt" instead of "Exit" when quitting software? Personal is where to put it.