How to setup the router and the clients for achieve this task?
That depends on the router. On low-end routers, it may be impossible to have the router do anything but ignore one of the subnets. On more flexible routers, you may be able to assign a "secondary" address to the Ethernet interface.
Can these network communicate each other?
If the router is the default gateway for machines in both subnets, it will route traffic between the two networks. Otherwise, normal unicast IP traffic will not pass directly between subnets. Broadcast traffic will be seen by all machines.
Which is the difference between this kind of setup and VLANs?
With a VLAN setup, the machines don't see packets for the other network at all. It's essentially as if they were carried over separate cables. VLANs isolate non-IP traffic as well.