I think an easier way to understand it - anyone can host a lemmy instance, and they will talk to other lemmy instances. It’s like if anyone could make and host their own subreddits on their own websites, and they would by default be accessible from Reddit.

So I have a lemmy.world account (and I think you do too), but the person you responded to has a lemy.lol account. We have accounts on different websites, but they use the same language and can talk to each other. We see this conversation on lemmy.world, they see the same conversation on lemy.lol.