The Mustang GT is the standard V8 version of the Mustang with a naturally aspirated, 300 hp version of Ford's "been around forever" 4.6 liter V8. Basically unchanged since 2005, although a 315 hp "Bullitt" edition was added this year, inspired by the movie car.
In comparison, the Shelby GT500 is still a Mustang, but it's upgraded by Ford SVT and licensed by Shelby. It uses Ford's 5.4 liter V8 with a supercharger and produces 500 hp. There are also upgraded versions: the GT500KR (KR stands for "King of the Road" like the '60s models) with 540 hp; and the upcoming GT500 Super Snake with 605 hp standard or 725 hp with upgraded supercharger.