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If connected to the same network wirelessly, does each console have it's own IP or is it the same? Like I know Public IP's are different, but what about Private?
When you log into your router from a device, it assigns a LAN IP address from a pool of IP's. That's just locally. The IP you see when you look at the network settings screen for your PS3 is not the IP that gets used when you connect to the internet.
Device -> Router -> Modem.
Your devices get assigned from the 192.168.1.xx pool to connect to your router, this is just to identify them locally. Any site or service you use is going to detect the IP address of your modem.
Sorry if it's a little scatterbrained, it's been a long day at work.