I think it has something to do with whether TouchDesigner opens one or multiple “sockets” on the operating system side of the connection. AKA Shared Connection would mean that TD just opens one socket externally (in MacOS or Windows network stack) and internally combines all the different OPs that are trying to access the network, as opposed to just opening a new “socket” or connection for each OP individually.
If my guess is correct, I would imagine which one you choose may only depend on very specific edge-case situations or devices that will or won’t work with one or the other. Personally, I have yet to see a specific re-produceable situation or a concrete difference between the two when flipping that toggle during “poke-in-the-dark” style troubleshooting, so YMMV.
I know that is basically useless advice, but mostly I just wanted to have a post in this thread so I will get a notification if someone smarter does post a better answer…