Remote desktop is a customary name for a group of applications that give a user the ability to access and control a computer from a remote location. Computers that are joined through a VPN act as if they are physically attached to the same switch. VPN allows computer programs that only work on a local network, to work on the internet.
Both of them are techniques used for accessing resources that are located in a remote location, but they are different in what you are allowed to access. A VPN is a smaller exclusive network that runs on top of a more extensive public network, while a remote desktop is a type of software that allows users to control a computer remotely.