Computer ?: IP address for laptop/desktop
 

Curious - If you have a desktop connected to a cable modem & have a wireless router attached to that setup -- when using a laptop with that wireless, does it present the same 'profile' (IP address, etc, etc) as the desktop - or is it visible as two completely separate entities?

The wireless router should have it's own DHCP server, and give the laptop it's own IP, while at the same time providing NAT (network address translation) to the outside, so the outside sees one IP

Outside will see one IP. Other traces may show though - such as cookies, exact browser/plugin versions, other client hints, etc. If ports are opened and forwarded, and that one IP is scanned, *many* different computers/services on different computers could show up, since each port could go to a unique machine running some other version of some service.

Edit - on your LAN though, each machine will appear as separate entities.

If you care.....
NAT
http://en.wikipedia.org/wiki/Network_address_translation

then look up mac address.