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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.

My understanding is a lot of residential isps would be angry at you for running servers of a substantial size out of your house anyways?

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.