When it comes to lamp shade fitters you have some options. Here is a quick break down of the ones used most often.
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You can use spider fitters, uno fitters or clip on fitters. They each have 2 options. For the spider fitters, you can get either a spider/harp fitter or a spider/reflector fitter. Spider fitters are used with lamps that have harps. Uno fitters have either a slip on fitter that sits beneath the bulb and is secured by the bulb. Or, you can get a threaded uno fitter, which sits above the bulb and is secured by a screw thread. Your other option is clip on fitters. Depending on the bulb you have, you can either get a bulb clip fitter or a candelabra clip fitter.
Slip-uno fitters sit beneath the light bulb.
Threaded-uno fitters are secured by the light bulb. These fitters are used for lamps that are facing down.
Harp-spider fitters are used for lamps with harps. They are secured into the harp by a fineal.
Reflector-spider fitters are secured by the reflector. As displayed below.
Candelabra Clip-on Fitters
Candelabra Clip-on Fitters are secured by clipping onto the candelabra bulb.
Bulb Clip on Fitters
Bulb clip on fitters are secured by clipping onto the bulb.