If you are using the FatFreeCart.com service, first please bear in mind that we provide that on a strictly do-it-yourself basis with no support whatsoever (that's a major reason it's free :^), so you're expected to troubleshoot any issues you may have with that. If you decide to upgrade to an E-junkie cart subscription (aka "FatFreeCart Pro"), that does of course include support. Since we don't officially provide support for FatFreeCart, we're not actually very well-versed in it, but that said, we will try to address your inquiry this time.
The two sites you referenced are actually using E-junkie Cart, not FatFreeCart. Although the two carts look and behave similarly from a buyer perspective, they are actually quite different under the skin.
FatFreeCart only allows for a flat shipping fee to be defined on each item, so if you want different rates to different destinations, you'd need to provide a separate Add to Cart button for each destination/rate. You can see this approach used in the example buttons provided on the http://www.fatfreecart.com/ homepage -- the "Buy my CD" item has two Add to Cart buttons under it, one for "Ship to USA" and another for "International Shipping.
If you subscribe to use the E-junkie Cart system, that uses a much more sophisticated and flexible Shipping calculator which asks the buyer to select their location in the cart and calculates shipping accordingly. This help page explains E-junkie's shipping calculation settings: