What does a computer use to determine if an ip address of another computer is on the same network or a different network?

It uses it's routing table. If the destination is on the same network, it transmits directly via the MAC address. If the destination is on another network, it transmits to whatever the table says for that network. For desktops it's usually a default address of the router on the computer's network.

Malware, not sure what else would fit that description.