But in those cases people actually hosted a server, right?

In discord it's more like a slack workspace, right?

The people "hosting" a discord "server" are not actually running hardware anywhere that runs the server?

98% of the people hosting "servers" of any kind in the world are not actually running hardware, everything is timesharing compute on a hyperscaler's computer now.

But yes, a Discord server is equivalent to a Slack workspace. It's just inherited terminology.

Correct, they are not hosting. It's a service. Still, an admin of a Discord "server" has complete control over the server - access, permissions, roles, etc.

For what it's worth I never actually hosted a ventrilo server either, I always just paid a service to do it. Pretty much the same experience as discord is today.

That's correct. Discord co-opted established terminology for its own ends and it was very successful.