networking

Is it possible to tell the difference between 2 computers behind a router running a piece of software, compared to 1 computer running 2 instances of the software?

Both computers have the exact same IP address according to whatismyipaddress.com, and both give the same exact results in an IP lookup.

Presumably they're behind NAT, if they have the same external IP. The router can tell the difference because it's aware of their MAC addresses, but if you're outside the LAN with no direct access to the router, all you can do is probe for different behaviors. There's no direct way to tell them apart.