Lamp shade stand are mounted on the lamp socket so you can use a lampshade with large ring (see figure below). This means that the lamp shade rack act as a holder for the lamp shade.
It is often advantageous to use a lampshade rack instead of a lampshade with fixed stand, because the lampshade stand provides a better opportunity to adjust the height of the lampshade over the lamp. Lampshade rack / lampshade stand can be adjusted up and down, so you can set the perfect height for the lamp.
The lampshade rack is available in two sizes - one of 40mm and one of 34mm. New sockets with socket rings should use a lampshade rack of 40mm.
Older lamps do often have a socket without socket rings, which means that you should use a lampshade rack of 34mm. If you measure the diameter of the socket, you will know whether the lampshade rack has to be 40mm or 34mm. The diameter of the top of the lampshade rack, where you place the lampshade, is the same (10 cm) of both lampshade racks.