Have laptops got two IP aresses?

Yes. Since you only have one actual internet connection (modem), your router does something called Network Address Translation. The router is the only device with a public IP address, so it creates a local network using the specially-allocated 192.168.x.x block of IP addresses (every single home network in the world either uses that or uses 10.x.x.x). When you want to actually do something on the Internet, your computer sends a message to the router, and then the router sends it on to the actual destination.