Do I need to use a particular terminal server with a particular client?

The type of terminal server you need is determined less by the type of network and more about what features you need. Windows Vista can connect to any generation of terminal server because they all use the RDP protocol but will get most utility from Windows 2003 Terminal Services or, when available, Windows Longhorn. The reason for this is that the user session is a combination of functionality on the client and server, and the least common denominator controls.

The short answer? You don't have to use a particular generation of terminal server with a particular client, so long as they can both connect via RDP. However, the most current versions of both client and server will give you a better user experience.