I am running a VNC server (vnc4server) on a Ubuntu server.
Does killing the VNC server itself kill the processes on it, such as applications started from VNC sessions?
I am running a VNC server (vnc4server) on a Ubuntu server.
Does killing the VNC server itself kill the processes on it, such as applications started from VNC sessions?
If you're using Xvnc, yes, because it contains its own copy of the X server and hosts its own graphical sessions. Terminating the Xvnc server will terminate any applications started in client VNC sessions.
Otherwise, no (unless the VNC server shuts down the X server or sessions on exit), because the VNC server merely interfaces with an existing X server to supply a remote desktop to the client. Klling the VNC server will not kill any programs started in VNC sessions, as the underlying X server and desktop environment are not dependent on the VNC server. Of course, if the server is killed, clients will not be able to access any running sessions.
If by "VNC server" in "running in the VNC server" you meant a server (operating system) which is (was) running a VNC service then the answer is: no.
Unlike for example the SSH deamon which opens new sessions when users connect (and the processes that users subsequently run become child processes), VNC server only shares the screen and allows the control of the machine it is running on, but it is running "side-by-side" with other processes.
Killing VNC server stops the sharing service and would kill VNC client session(s), but does not influence other processes running on the server (operating system).