what they mean is,
when you change down and let off the clutch, the engine has to revved up by the drivetrain. and this imparts a braking force to the rear wheels (since the engine doesn't want to speed up with no throttle), and if you let off clutch too quickly, it causes the wheels to slow down to less than the speed of the car. the wheels don't stop, they will only go to the speed determined by the engine, but they may lose traction.
in trucks, because they have no throttle, they have "compression braking" but that is different.
sounds like they just used whatever terms took their fancy at the time?
Bookmarks