Anyone and everyone can run their own Nostr server if you'd like. Discord is similar in this regard, but it's all Discord's servers with their rules and their guidelines. Nostr is different because there is no central company that is in control. Users are in control. It's a protocol built by users for the users.

It's still more like Twitter/X or Facebook, except instead of sending/receiving posts through just their servers, you send/receive to many servers run by multiple people

The main difference is that you can physically own and control your own relay. Discord can shut down your server on a whim. Nostr cannot.