Think of it like email.

The email provider is the instance:

Google, Yahoo, outlook, etc

The community/user is your email address:

Android@gmail, Android@yahoo

Because they are different providers you can have the same name since it's the only one on that provider.

A subreddit can be uniquely identified like this /r/games. Once that name is taken, no other sub can have it.

A Lemmy community is identified like this: [email protected]. Notice it has a name part and a server part, both are necessary to uniquely identify the community. [email protected] is a different community with different mods and different posts/comments (unless someone crosspost, but then it's still two different posts with mostly the same text inside). You can mostly access any community on any server from your account, mostly irrespective of what server your account is on.

But similarly named communities on different servers are different communities. They are analogous to /r/DnD vs /r/dndnext. Similar topic, different subs, same with those Lemmy communities.

Yeah:

Instances = Servers

Communities /c/ = Subreddits /r/

Basically, yes. And it's not too much of a stretch to think of lemmy.world and lemmy.ml as two separate Reddits that share with each other, so anyone on either one can access stuff on both.

So two communities that both have the same name but are on different instances are actually two entirely separate places since they're on two entirely separate "Reddits". One is [email protected] and the other is [email protected].

Yes, essentially.