You may have seen the term "speed boost" in relationship to some adapters. Indeed, Speedbooster is the brand name of one such adapter. What's going on with these, and why are they different than other lens mount adapters?
Most lens mount adapters are just hollow tubes with the proper mounts at both ends, and sometimes electronics that translate from the front mount to the back mount (and vice versa). A "dumb" adapter is just a hollow tube without electronics, and often requires that you make settings on the camera body to use them at all. The "smarter" versions that include electronics pass on focus and aperture information, as well as other information that may show up in the EXIF portion of an image file.
The speed adapters are not hollow tubes. They have optics in them that perform what is called focal length reduction. For DX, that's typically a focal length reduction of 0.75x or thereabouts (multiply the actual lens focal length by that amount). If you're fast at math, you'll quickly see that's the inverse of 1.5x, which is the crop DX makes from FX lenses. Thus, put a 24mm FX lens on one of these special adapters and you get the equivalent of a 16mm DX lens. In other words, the FX field of view without the adapter would be the same as the DX field of view with it.
Besides the focal length change, these adapters manage a different trick: the increase the effective aperture by about a stop. After all, aperture is a ratio of lens opening to focal length; the lens opening didn't change, but the focal length did, so, boom, faster aperture.
The Zhongyi (Mitakon) Lens Turbo II is one such adapter. You can get versions of it for Leica M42 to Z-mount, Canon EF to Z-mount, and Nikon F-mount to Z-mount. Note that these adapters do not have electrical contacts, so your lens will be manual focus and you have to set apertures on the lens. Each version is US$149 and weighs about 233 grams.
Metabones also makes such an adapter: The Nikon G to Nikon Z-mount Speed Booster ULTRA, which sells for US$479 and has a manual aperture control built in.
Finally, Kipon makes such adapters for Medium Format lenses: plus Baveyes focal/reducer (0.7x) adapters for Pentax 645, Pentax 67, Mamiya 645, Hasselblad V lenses.
