Hi,
routed mode:
The CSS acts as a router, it routes packets from the client to the server. The server has the ACE configured as default-gateway.
There is a client-side VLAN and a server-side VLAN. These VLANs have different subnets.
Bridged mode:
The CSS acts as a bridge, it switches frames from the client to the server. The server has the upstream router configured as default-gateway.
There is a client-side VLAN and a server-side VLAN. These VLANs have the same subnet, but different VLAN IDs. The ACE bridges the client traffic from the client-side VLAN to the server-side VLAN.
Bridged mode would be most used in case one cannot change the servers IP addresses, or if address space is an issue.
Hope this helps.
Kind regards,
Dario