Terminal service is client server environment where one computer acting as a terminal server which will serve the requests from the TS clients. This can be two modes one is Application Server mode, the other is Remote Administration mode. The former is used to access the applications on the server which requires licence and the later is used to remote administration which does not require licence.

Remote Desktop sharing is similar to Terminal service's Remote Administration mode.But the diffrence is there is no client and server environment. This is simply used to share one another's desktop in the network