With Terminal Services, many people log on to the same server to run their applications, but they are running their sessions on the same server as many other users and are running a server OS.
The difference between Terminal Services and VDI is isolation. The isolation is at the session level with Terminal Services. With VDI, each user connects to a separate, virtualized OS instance, so the isolation is at the OS level.
Check out this video by John Savill for more information about VDI.
Check out hundreds more useful Q&As like this in John Savill's FAQ for Windows. Also watch instructional videos made by John at ITTV.net.