There is a local or <b>private</b> IP address assigned to most computers. This is what you see when you run the ipconfig command. When you visit a website, your communication goes through a router or firewall that has a public IP address. It is this <b>public</b> IP address that you see and will be logged when visiting a website. This feature is called network address translation (NAT) or can also be known as port address translation (PAT).
Check out this Howstuffworks article on: How Network Address Translation Works
More technical information on NAT can be found here.
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