What is a mechanical zoom or mechanically-linked zoom lens?
They are both the same. They are lenses which are optically zoomed by hand. This is nearly always done by rotating a ring around the lens barrel. Mechanical zoom lenses are very efficient because they move immediately, they have no zoom-steps and they do not require a zoom motor (meaning they don’t use battery power). These lenses can be controlled with complete precision as fast as you can turn your hand.