Communities with the same name on different servers?

How do communities work across servers? For instance, I registered my account on server A, and create a community named MyCommunity on Server A. Someone who's registered on Server B can access MyCommunity by going to !MyCommunity@ServerA.

Now if someone else on Server B decides to create a community also called MyCommunity on Server B, I could access that by going to !MyCommunity@ServerB.

My question is, with the MyCommunity communities ever sync across Server A and Server B? Or will they remain completely separated since they're on different servers? Will things posted to !MyCommunity@ServerA ever show up for people that have only subscribed to !MyCommunity@ServerB, or are these kept completely separate?