[ycombinatrix]

>Doesn't Discord require every user to create a new account, even if they're already using Discord in some other community?

No, the same account is used. You get prompted to choose a nickname each time you join a server though.

>So when they say "a Discord server", they really mean it--they're like droplets running independent deployments or whatever

No, they're probably all run on the same compute. The "official" name for a discord server from the API documentation is actually a "discord guild" and it works pretty much like a subreddit.