Private meaning only certain people can use it, maybe it's paid, maybe it's for your family, maybe it's for your community group. This could be something like nostr.wine or a WoT relay or something much smaller. Personal would be just for you, essentially s backup of all of your events and more. This would be something like a #Haven relay.

I guess it's personal since I'm the only one to use it. I'd run a full relay but honestly I don't know the implications of "c" p content nor do I know how to protect against it.