In my neck of the woods, the common word for making something out of wood is "carving." "Whittling" generally means destruction of a piece of wood with a knife.
The only use I've seen for it is making trinkets (paper knife anyone) out of wood. Like carving but less refined, only using ones general duty knife not carving tools (chisels, etc.). Like scrimshaw but using wood only and not spending so much time and care.