Well, in conclusion it is quite easy to explain - as higher the numbers, as closer to the original road-car. But in detail...
GTRX is a fictional supercar GT class, which is theoretically the fastest of those available. GTR1 is a now-defunct real life class for cars such as the Ford and Saleen, that raced against the Aston Martin DBR9, Corvette C6R, Lamborghini Murcialago etc. It died due to lack of new interest in 2011. GTR2 is based on rules similar to the GTE (formerly GT2) class at Le Mans. The RUF is fictional and the Corvette and BMW have been replaced by newer models in real life, but these cars ran in a class famous for the likes of Ferrari's 430 and now 458 and Porsche's 997 RSR and now 991 RSR. In real life, these cars run at Le Mans as well as Daytona and Sebring in the US 'TUSC' series, usually alongside prototypes. GTR3 is based on the global GT3 ruleset. In this class, the cars are faster in a straight line than the GTR2 cars but have less mechanical grip, so achieve similar lap times. In real life, this is a class without rules and the cars are matched together through a process called Balance of Performance, which is why there is such amazing variety. These are the top class of car for races such as Nurburgring 24 Hours, Spa 24 Hours, Bathurst 12 Hours and the Blancpain Endurance Series.