The ownership is besides the point here. The point is the Wordpress installs don't talk to each other, neither do Discord servers, behind the scenes. Discord's servers aren't one giant big powerful computer, it's a lot of smaller ones. Behind the scenes, each Discord "server" exists separate from all the rest of them. After the load balancer, the StableDiffusion Discord messages don't intermix with the Midjourney Discord messages, so their internal architecture can be that each "Discord server" is self-contained to it's own group of servers that don't talk to other servers. (Discord's decision to call them servers here is really unfortunate and confusing.)
This means that for scalability reasons, it's easy to create a new "Discord server" as it only has to be connected to the other people on that server, and not the whole rest of the Discordverse.
Twitter has no such luxury. So when that one cat video goes hella viral, the system as a whole needs to handle that access pattern, which is actually difficult to scale. We'll have to wait and see how the site handles the world cup in a few weeks, as that is an event that stresses the service.