This is from their wiki site for more clarification Kodi is a media center application and OSMC is the operating system that runs Kodi and brings it to your de

This is from their wiki site for more clarification Kodi is a media center application and OSMC is the operating system that runs Kodi and brings it to your device. OSMC is not a fork of Kodi but rather a Linux distribution that ships Kodi as the main application. This is a similar concept to Kodi running on top of Windows or Android. OSMC is based on Debian Jessie (a flavour of GNU/Linux) and has been heavily optimised to provide the best TV experience possible.