How bridge group is differentiated from vlan

Bridge groups provide a method to group two or more ports into a single broadcast domain, where as VLAN provide a method to group many ports into a single broadcast domain or establish a number of broadcast domains (or secure groups) on a single switch.

Bridge groups operate at layer 2. So they are not very effective at connecting layer 3 switches and routers. If you want to connect 2 ports of a layer 2 switch with 2 Ethernet interfaces of a router you can do that but the Ethernet interfaces on the router no longer operate as routed interfaces.

Refer to Understanding and Configuring VLAN Routing and Bridging on a Router Using the IRB Feature for more information

The bridge-group command is used to configure a Cisco device to bridge traffic between two interfaces. For example, you wanted to join two LANs – connected via a router and a serial link between them – together, you would configure the LAN and WAN interface on each router to be part of the same bridge-group. This will create a bridge between the two LANs and Ethernet packets from one LAN will be visible on the other. If you put bridge-group on both interfaces then they become part of a single broadcast domain.

LAN 1—-> [Router 1] —-> [Router 2] –>LAN 2

On Router1:

int fa0
bridge-group 1

int s0
bridge-group 1

bridge 1 protocol ieee

On Router 2:

int s0
bridge-group 1

int fa0
bridge-group 1

bridge 1 protocol ieee

Refer to Configuring Transparent Bridging for more information.