Whittle is to make something, usually wood, little or to destroy by cutting small shavings, parsings or pieces. It gives reference to destruction, down sizing or reducing in size and carving. It also references other things like financial, business practices or an oppositions lead.
Carving can be wood, metal or about any material but also references similar to whittle. Lol.
I always thought of whittling as just cutting a stick down in size or just for something to do like fidget. Carving to me was making a shape or intended object like a horse or a flute.