Emby, a (somewhat) open source C# project, is not a fork of Plex Media Server, a closed source C/C++ project. Emby was forked as Jellyfin however, as a reaction to Emby becoming more and more of a closed source project.
That's what Plex does: it has server apps and client apps.
It is a nice feature for low bandwidth applications. Say a VPN to your phone, or a friends house who has crappy internet. If I remember correctly there were a lot of clients also for TV's which have absolute rubbish CPU power and no local storage (for holding metadata). Also the centrally managed metadata is nice when you have more than one client. You can get the same effect with KODI and using a DB like mysql or mariadb. But it is sort of finicky to setup correctly.
I personally use KODI as I do not need that particular streaming feature. Also it is broken with ISO's which is one of my major use cases.