LANs
Local Area Networks are devices in the same broadcast domain. The simplest separation is two have two separate physical switches, although this might lead to large inefficiencies given the need to doubling the equipment and configuration.
VLANs
Rather than purchase two separate switches we can use a single switch (and therefore config/power sources, etc) to manage the separation between broadcast domains using logical conditions.
VPNs
VPNs alow encrypted data to traverse a puiblic network.
VPNs connect to some device known as a concentrator, which is often integrated into a firewall