This is a really good question that I am sure will be answered with lots of technical answers. I will try and give my understanding of the difference in not so technical terms...
Race boards are for setting a turn then going straight to the next gate for a short turn then repeat. They also tend to have a flex profile that will accelerate through the turn typically with a stiffer tail. You may hear that they do not like to finish the turn.
Freecarve boards like to finish the turn across the fall line. This give you good speed control. They often have a forgiving flex pattern that work well in a wide range of carving conditions.
There are tons of tricks that different board builders do to blend designs for specific applications. Side cut, metal construction, core layup, amount/direction/pattern of fiberglass or carbon.
The magic of this niche sport is that we have amazing board builders available locally in North America (Sean @ Donek, Bruce @ Coiler, Mark @ Thirst, Prior) that will listen to your needs, watch a video of your riding and build you some magic if you listen to them.