XBMC, or Xbox Media Center, has been around for what feels like forever, but the developers behind it have just rebanded the service to Kodi Entertainment Center. Kodi will be the new name of XBMC from version 14 of the software, onwards.
Now that we have the rebranding in process, version 14.0 or "Helix" will see the developers owning the trademark of Kodi. This will prevent companies, especially Microsoft, from coming after the developers - even though there have been countless versions of the software have been released under XBMC. The new Kodi release is a rough alpha right now, so we shouldn't see the Kodi name spread far and wide for now.