That document seems to use communities in the normal English sense and spaces in the "collection of Matrix rooms" sense. I would say spaces are what they're called and a community is just an informal group of like-minded people who can be better-organized using spaces.
That isn't exactly a discord clone, though. More like WhatsApp but federated. At that point I'd actually just rather use matrix than a messaging app by that cocky dev.
I never became a discord guy, but it seems like IRC (not federated the same way lemmy/mastodon/etc are but functionally similar) would meet the requirements.
While it's probably not exactly what you're looking for, I wanted to give vibe coding a try and wound up making a discord like client if you think it might be handy. It's not actually a chat server, it's just a client that uses a chat style layout to display posts under the mastodon api.