Git is federated, as in Jabber. A branch has a place where it lives. If you do something with a particular branch, you need access to the place where it lives but not to anywhere else.

Monotone is distributed, as in Usenet. A branch may only exist on certain servers, but it is not logically tied to any one server (or set of servers). There is a global namespace for branches.

I think other systems (hg) tend to be more like the Git model, because permissions handling is far simpler.