The idea of thin clients wasn't a Microsoft invention. If anything, Terminal Server was a stab at delivering an alternative to the Unix world's X Window System (more on X below) that could be tied to Windows and therefore bring in licensing revenue.
In the second half of the 90's, everybody and their dog was trying to deliver thin clients under the buzzword "Network Computer". An NC was a graphic terminal on a fast network driven by a remote computer system. Larry Ellison of Oracle famously predicted that NCs would quickly replace desktop PCs, and even tried to buy Apple at one point in order to make that happen.
Oracle and Olvetti, an Italian computer company, created a joint research lab that developed a handheld tablet NC called the Videotile. The hardware never took off, but a virtualized software version, VNC, managed to escape the lab. AT&T actually bought the research division and released the VNC technology they had developed as an open source project.
Today there are VNC clients for nearly everything from Windows to Linux to Macs to Palm Pilots, making it one of the more successful examples of releasing abandoned technologies as open source.
VNC delivers remote desktop functionality in a simple and open way, but like Microsoft's RDC client, it only delivers a remote screen, not the output of a specific application; that capacity was addressed by Unix workstation vendors using X Window, NeWS and NeXT's NXHosting.
Unix workstations: selling platform solutions