Your system will have two types of IP address - internal and external. The router will have an external address to connect to your service provider. When you whatismyip.com it will report this address - which will show as the same for both pc's. Each of your pc's will have an internal ip address - these will be allocated by your router and will be different for each of the two pc's.
It would be helpful to see exactly what addresses are being assigned on your system. You can find this by going to start programs, accessories, command prompt. At the command line enter this command:
ipconfig /all >desktop/ipconfig.txt
This will create a short report called ipconfig.txt on your desktop. If you wish you can then post the file on here and we can help you interpret it.