You're both partly right but missing one vital piece of information: the server must be running Windows Terminal Services, which is a component of Windows 2000 Server. If it's an NT Server, it actually needs to be a specialised version, Windows NT4 Terminal Server.
Once the program is installed and correctly configured on the server, a Terminal Services session needs to be set up. Basically, you need to define on the server that the program is to be made available to PCs on the network and how many licences (sessions) will be made available.
On the PCs on the network, I think you need to install a small Terminal Services Client application so that it understands how to run a program that is actually installed on the server. Then, you need a shortcut on each PC to the program(s) on the server that can be run remotely.
NOTE:
When you run a program remotely, it actually runs it on the server and takes up the server's resources (memory, processing time, etc). All that the client PC does is displays an "image" of what is being run on the server. Lots of clients can run the same program simultaneously because they are managed in separate sessions so one user will not see what another user is doing. However, they each need their own memory resources, processor power, etc, so a Terminal Server is usually a separate high-spec machine that, when under heavy load, will not impact other services like file/print sharing, email, Internet access, etc.
I only have a basic knowledge of Terminal Services, enough to understand the theory rather than to put it into practice myself. However, I'm sure that the Microsoft Technet site (
www.microsoft.com/technet) will have articles and 'white papers' to help you decide whether it's what you want or not.
Hope that helps