When it comes to Matrix, I have trouble making the parallel. Maybe because of the terminology?

It’s almost identical on Matrix, although many clients make it hard to distinguish things. For example, Fluffy Chat (and the “official” Element too, I think?) show both Servers AND their Rooms on your “all chats list”, making finding things confusing.

Check out Commet, it structures things exactly like Discord, so you’ll clearly see what’s a server, what’s a room on that server, etc.