VPN stands for Virtual Private Network, while VNC means Virtual Network Computing. VPN is a network implemented, which permits large network area, such as internet user's connection to behave as if it is connected to the same switch. VNC is a network implementation which can be used to move the desktop of a computer to another computer with the use of the network computing. VPN is a version that is more advanced which functions very similar to the tunneling protocol. It permits the connection of applications that can use the local network, but it cannot connect via the internet to function.
Garena and hamachi are good examples of these. They are generally VPN software's, but Garena deals more with gaming. VNC can be used to access your desktop from another location, or if you want to access files on your computer through another computer. VPN is a way of creating a private network over a large public network, while VNC is a means of accessing and control your computer through another computer via the use of Ethernet.