In a nutshell, the higher the number, the more it resembles the performance of the production version.
For example, the GT3 class race cars have a simpler form of aerodynamics- ie. front splitters, rear wings, air-dams etc- then the GT2 class racecars. It also means that the car body/chassis cannot be (highly) modified from its original form. This result in lower downforce in the GT3 class although both classes have pretty much the same power output/weight.
And in the highest class, GT1, the bodywork retains very little of the original production model. What you end up with is a car with a very sophisticated aerodynamic and a lot of downforce.
There are also regulations regarding brakes (only GT1 class is allowed carbon brakes) and even drivers and teams- GT3 and GT4, for example, is more geared towards novice/gentlemen drivers and privateer teams while GT2 and GT1 are for seasoned professionals and works teams.
Of course, these barely touch the surface. The regulations are more complex and encompassing and for that you need to go FIA website.