I made a quick design of the LN topology, of how I see it.
I hope will make more sense for you to understand the levels of rings we have:

PUBLIC RINGS

• central big beefy profitable nodes, with large liquidity and strong servers
• LSP ring, medium sized public nodes, connected well with these big nodes, offering good routes to mobile nodes users and also to pleb rings
• All custodial accounts public nodes (Alby, WoS, Strike, Cashapp etc)
• Plebnet Ring, with smaller liquidity capability and machines, maybe in process to became LSPs

PRIVATE RING

• outside rim, the private ring of mobile nodes, connected to well known LSPs
• normal small pleb private nodes, trying to evolve

https://m.stacker.news/25790

It's all about WHERE you position yourself.
As you can see the out rim cannot communicate directly between them, but only through good LSP nodes.
All the rest could be interconnected through public channels.
Also the LSP nodes could have PRIVATE channels (that the public do not see it) to big beefy nodes, but mostly public channels.