What mark_boyle2002 said, except that if they do not match, your are either going through a proxy server or are behind a NAT device. They are not the same thing, and depending on what you're trying to do, the difference may be significant. (For instance, proxy servers will typically rewrite your HTTP headers, whereas NAT boxes will not. [Further digression: a NAT device operates on layer 3 or 4; the network or transport layer. The web proxy operates on layer 7; the application layer.])

Telling if you're behind a NAT device, a web proxy, or both is a little tricky. Here are some hints:
  • If your machine's IP address (in the control panel/ifconfig/etc., not from www.myipaddress.com) starts with 192.168 or 10, you are behind a NAT box (and possibly also a web proxy). These addresses are not routable on the internet, so the NAT device is obviously transforming your packets on the way out.
  • Some servers run software that tried to detect whether or not you're behind a proxy. The sites seem pretty unstable so I'll just link to a helpful Google. Of course, a sneaky web proxy cannot easily be distinguished from a NAT box.