VNC, a bit less laggy

Does anyone know of something similar to vnc, but everything possible is run on the client’s computer?
For example if you start a vnc session, the desktop environment would be on client’s computer, the file browser on client’s computer. When running a terminal or a file browser, it would interface with the server and for example if you open a text file, after saving it, it would modify the file on the server.

You don’t ask for VNC, you basically want what NFS can do. You do everything on your computer, but if you modify something on the NFS mount then it automatically gets modified on the remote computer, as well.