The server is not usually a remote machine. The server is the app accepting remote connections.

This has been true for decades.

https://en.wikipedia.org/wiki/Server_(computing)

Please don't imagine that I don't fully understand this.

Nevertheless, X11 "server" and "client" have confused very smart and highly technical people. I have had the entertainment of explaining it dozens of times, though rarely recently.

And honestly, still, a server is usually a remote machine in all common usage. When "the server's down", it is usually not a problem on your local machine.