Difference between Layer 2 VPN and Layer 3 VPN?

Layer2 VPNs virtualize the datalink layer, so that for example geographically separate locations appear as if they were operating in the same LAN or physical connection.

Layer3 VPNs virtualize the network layer (routing table) so that it may be possible to route your “internal” networks over a public infrastructure such as the Internet or Service Provider backbone.