Yes they do. Please look at the screengrab below, used gratefully from Cicsco systems. In the image you can see the engineering VLAN is on three different networks but treated as one logically grouped domain. Please notice there is a connection between all the networks.VLANS are pretty cool and hold many advantages but Im still a bit unclear on them. Do the LAN switches all have to be physically connected to each-other in order to set up A VLAN network?
If you had 20 computers in your house, and all were connected to the same LAN, you could use a VLAN to have "gaming computers" and "mom's home office computers". These devices would be virtually segmented, each having a different IP address range (for example, maybe your gaming computers would all have IP's starting with 10.2.x.x and your mom's home office would have 10.123.x.x) but the computers would be physically connected.
Hope this helps.