Actually GT is just an abreviation. It was developed to be used as an abreviation for a professional road racing classification known as Guran Tsūrisumo. Guran Tsūrisumo is Italian for "Grand Tourer" or "Grand Touring". The 1st GT class car was a Ferrari. Ford began developing a GT class car for international racing in the early 60's and used the Mustang chassis.
The US car market now uses the "GT" badge very loosly. They use it to make the car buyer know that the car can be used as a "sport touring" car. As appoused to a Luxury car or a sports car.