Remote Desktop lets you control a computer remotely. You can run programs on the remote computer, using the remote computers CPU. Within the RD session, you can access files and program installed on the remote computer or network resources that the remote computer can see. If you copied a file to the desktop in a Remote Desktop session, you wouldn't have copied it to the machine you're sitting in front of, but to the one you're controlling.
A VPN is simply a way of connecting your local computer (the one you're sitting in front of) to a remote network, and having it appear as a local machine. AFAIK you get assigned an IP for the LAN you're connecting to. You could then use Remote Desktop over your VPN... It would be like using Remote Desktop from one machine in the remote network to control another machine in the remote network. The VPN just "fools" the network into seeing your local machine as a machine in the remote network.
I hope that's right, or I'm going to fail my Nework+ exam next week

Anyway, the more you look into it, the more complicated it gets. There are all sorts of things like Remote Access vs Remote Control, RDP, VNC, Direct Access Servers, RRAS, Remote Desktop Services Servers... and I'll be damned if I know exactly the differences between them. Hopefully someone here does
