Hello,
The ip default-gateway is a command to define a default gateway for a Cisco IOS-based router or a switch that operates in the host mode. A router or a switch operates in the host mode if it is configured with no ip routing command and has no routing table as a result. For Catalyst switches such as 2950, 2960, 3550, 3560, or 3750, the host mode is the default mode. Routers operate in routed mode by default. If the device operates in routed mode, the ip default-gateway command can be configured but will be ignored. In that case, the default gateway can be configured with ip route 0.0.0.0 0.0.0.0 or by ip default-network.
The ip default-network is a deprecated and old command whose purpose was to designate a known classful network as being already located in the "outside world", and so the route to that network would be also considered a default route. If you had a classful network in your routing table that was marked as a candidate default network using the ip default-network, then all packets with an unknown destination would be sent down the same path as packets for the candidate default network. This command should not be used anymore as it only works with classful networks, does not cooperate well with routing protocols, and is very cumbersome to use.
You might be interested in reading the following document as well:
https://www.cisco.com/c/en/us/support/docs/ip/routing-information-protocol-rip/16448-default.html
Feel welcome to ask further!
Best regards,
Peter
