@mmn In any email application and in Pump.io also there is a notion of an Inbox. The Inbox (close to Home in GNU Social...) holds all messages, which the server-side system ("Social network") thinks should be delivered to the User. It's a client configuration matter, if this Inbox/Home is presented as one stream or some messages should be filtered out into another stream/folder/timeline...
I mean, nothing is set in stone...