All of the manufacturers ratings apply individually & collectively. If you're trying to comply you can't exceed any. The combined weights, the GVWR including the pin weight, the axle ratings and the tire ratings, all must be monitored and complied with.
Which one is likely to be the controlling factor (first exceeded) depends on your specific truck and loads. for single rear wheel trucks hauling a heavy 5'er, its usually the GVWR that limits you, since the loaded weight of the truck plus the pin weight of the RV usually exceeds the GVWR before it gets close to exceeding the axles or GCWR, especially with the extra weight of a diesel engine or 4x4 option. The GWVR is usually less than the sum of the 2 axle ratings, since the weakest link in the chain determines the rating value.
You see lots of overloaded trucks on the roads because not everyone pays attention to these ratings. some just don't care, some think its ok if you're within 20%; some think its ok to exceed GVWR as long as you don't exceed the axle rating. everyone has their opinion and you'll hear a wide range of them here. go to any official source and its clear the intention is to require all of these ratings to be complied with.