They are entirely different.
VLAN is a virtual network, configured using software.
VLAN is where the network consists of a series of machines that act as though they are all on the same local network wire. The machines may all be on different areas or subnets of the LAN they are on but the VLAN software allows them to operate as though they are one network.
VPN is a Virtual Private Network - it is where information is passed securely frmo point to point (nodes) over public wires, like the internet.
VPN is an ecrypted channel through which you can pass information. It is comparatively slow since every bit of data is enrypted before passing through and decrypted at the destination point.
It basically allows you to connect two (or more) points over a network that is inherently unsecure (the Internet) by establishing a private encrypted tunnel that runs over the public network between the two points. Everything you send through VPN is, by default, secured against public access.
The above is a vast oversimplification but it covers (barely) the nuts and bolts of the two.
Some Googling will give you more information than you probably want.
And yes, you can run VPN through VLAN but we're sailing off into some very deep water here and I'd rather not start hammering out an explanation of how that works on a Friday afternoon...