These actions of sidespin and shot curvature happen because the clubhead rotates around its vertical center-of-gravity axis whenever the ball is hit off the toe or heel.
When the head rotates in response to a toe-hit, the ball slides, then rolls, sideways across the face from the toe toward the center of the face. This causes the ball to leave the face with a hooking or draw sidespin. Conversely, when the head rotates the other direction in response a shot hit off the heel, the ball slides, then rolls, sideways across the face from the heel toward the center of the face, which causes the ball to leave the face with a slicing or fade sidespin.
The reason all woodheads are designed with a horizontal curvature across the face (called "bulge") is because of the gear effect. If shots hit off the toe generate a hook or draw curvature, the face needs to be radiused (curved) horizontally so the toe shot will leave the face angled to the fade side of the target. Thus the bulge radius causes the ball to start off more to the right (for a right-handed golfer; or to the left one a toe shot by a left-handed golfer), after which the hook spin generated by the gear effect takes over to bring the shot back toward the center of the fairway.
For shots off the heel, the bulge radius across the face of the wood causes the ball to take off to the left (for a right-handed golfer; or to the right from a heel shot for a left-hander), after which the fade spin generated by the gear effect takes over to bring the shot back toward the center of the fairway.