There are actually several reasons. First, an IP address is assigned to every network interface on the computer. So if you have both a wireless NIC (including built in wireless) that's connected to a wireless network and an Ethernet card that plugs you into the wired network, you'll have two different IP addresses, one for each. The two will also have different physical addresses (MAC addresses). Although both of the interfaces use TCP/IP, the TCP/IP properties for each is configured separately, too. Thus, your wireless connection might be set to use DHCP to get an IP address automatically, whereas your wired connection (usually called the Local Area Connection) might be set up with a static IP address (one that you type in for it).

Even if you only have one network interface, though, you find that the IP address reported by the ipconfig command is different from the IP reported by web sites such as http://www.whatismyip.com. That's going to happen if you're behind a NAT (network address translation) device, either on your local network or through your ISP. Computers on an internal network behind a NAT have private addresses (usually starting with 192.168.x.x, 10.x.x.x, or 172.16.x.x), which the NAT device translates to a public address that is recognizable on the Internet. Ipconfig will return the private address assigned to your computer (for example, 192.168.1.25), but WHATISMYIP.com - and other similar web sites - will see your IP address, and that of all the other computers on your internal network, as the IP address of the NAT (for example, 64.24.2.18).