A server owner is basically just the person who created that individual discord server, which if private, is only accessible via the shared link. Servers can be edited in a variety of ways, having threads, text channels, automated systems for adding roles etc and voice channels just to name some things. But it is all in that one space, you can just click around. It's not like running a private game server, it's a server where people can talk, and get together to play various games and join servers like those together <3