You know public.
Moderated, is.. moderated. Comments, maybe even approval of who joins, that kind of thing. Basically, it has enforced rules - where a public group may not.
Invite only, obviously, invitation to join only. Not by the creator, but by whoever has the power to do so. For example, in the military, Sniper School is invitation only. If you get high marksman scores, they may be interested in you.
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