This seems like a distinction without a difference. If you used a paid service offering Mumble servers that used some custom software that allowed them to offer multiple ... "servers" on different ports/IP addresses from a single daemon, would you really care?
Focusing on the fact that it's not really a "server" because they aren't running as separate processes seems like utterly silly pedantry, and we probably don't even know if that's actually true regarding Discord or not.
A server, to me, you have control over if that's the product name of what you rent. Discord servers are as much yours as Hacker News is yours
It's like pretending a taxi is the same as owning a vehicle, even if the taxi company was your neighbor and there's always someone available. The result is the same but the distinction couldn't be clearer. To me it's similarly misrepresentative to say you own a car when you live next to a big taxi station, as to say the SaaS web front-end you get on Discord is a rented server
The distinction matters. The cost (to my users) of switching from one Mumble server to another is the same, regardless of who hosts the server. The cost of switching from one "Discord server" to another is much lower than the cost of switching between Discord and any Discord clone, keeping people on Discord.
No, it's a feature of Discord putting all the "Discord servers" into one program, but not allowing third-party servers to be listed in the same program. A rival system offering exactly the same featureset as Discord is nonetheless not interoperable with Discord, whereas a Mumble rival could easily be interoperable with Mumble clients.
Focusing on the fact that it's not really a "server" because they aren't running as separate processes seems like utterly silly pedantry, and we probably don't even know if that's actually true regarding Discord or not.