Tree Cutting is for cutting down trees, turning logs into planks, and a few other things.
Wood sawing is for shaping wood into usable items, for example wooden wheels, beds, barrels, etc.
If you change the (m)ode while looking at recipes, you can see if a project will yield any by products like splintered wood. The most reliable way to get splintered wood is to (s)mash wooden objects.