Easy, the GT3R is the race-only version of the GT3. It's gutted a little and equipped with a roll cage as well as a few other races perks, but that's the only difference. The whole purpose of the GT3 was to race it in the GT3 class. The street versions (Just GT3) are the cars needed to homolgate the GT3 as an actual car (I forget the number needed, someone will know).
There's also the GT3 RS or Rennsport, which is just another race version of the GT3. They are used quite extensively all over the world.