This video from the 1930's highlights several logging tasks. It also captures the transition from horse or oxen teams to gas tractors or trucks for transporting the logs.
Undercutting: notching the tree to guide the direction of the fall.
Falling: cutting the trees to bring them down.
Bucking: cutting the downed trees into more manageable lengths (logs).
Limbing: removing the limbs from the trees.
Skidding: moving the downed logs to the transport vehicle (usually via rough trails called skid roads).
A complete list of definitions is available here.