You can have multiple users logged into a Windows computer at the same time, each with their own programs running. However, unless you're running a Server edition of Windows, multiple active logon sessions are not possible. In other words, you can have a local and remote user both logged on, but only one of them can be active at the same time.
So in this case, if you log in user A at the physical computer (console), then log on user B remotely, user A would be disconnected. His programs would still be running, but the console would show a message stating that the computer is in use by user B. If user A unlocks the machine, the opposite would occur, and user B would be disconnected but his programs would remain running in the background.
One alternate approach, if you need multiple interactive logon sessions to the same physical computer, would be to install a virtual machine on the computer and run a second instance of Windows (or other OS if you prefer) and connect to that remotely. Of course in the case of using Windows you would need a second OS license.
Server editions of Windows support Remote Desktop Session Host which with proper licensing allows for multiple simultaneous interactive logon sessions.