The story is that the 'functionality' you are looking for is kind of behind the scenes. When you choose a type of community (open, restricted, private, or inherited) you are actually choosing the initial permissions for the space.
Example: Settings of Restricted vs. Private
Restricted: Navigating with Admin Console to Spaces -> restrictedSpac -> Permissions -> Space Permissions you will see red x's in the 'anyone' users and green check marks for most of the 'registered users'
Private: Navigating with Admin Console to Spaces -> privateSpac -> Permissions -> Space Permissions you will see red x's in the 'anyone' users and in the 'registered users'
So the 'functionality' is the permissions set up for the community.
I think the language on those options is off: we don't have a feature that gives users the ability to 'invite' another user or 'approve' a user. I created an issue to change the language:
Thanks for pointing it out!