Some history. In WWI, the US found that the standard M1911 pistol could not be made in sufficient quantities so they asked Colt and S&W to make revolvers that could fire the standard .45 ACP ammunition. Since the .45 ACP is rimless (having an extraction groove), it would simply fall through a normal revolver chamber. But S&W came up with the idea of putting shoulders in the revolver chambers to support the round, and a clip that would hold three rounds, making it possible to extract fired rounds as well as to load the gun quickly. Those three round clips were called "half-moon clips." But their use required more room than the standard rim of revolver rounds like the .45 Colt, so some metal had to be removed from the back of the cylinder.
In modern revolvers, used with rimless rounds like the .45 ACP or the 9mm Parabellum, the cylinder is trimmed down, just as with the older guns, but the clips are now usually "full moon clips" holding six rounds (more or less, depending on the revolver design and whether clips are available).
Clips are not needed for extraction of conventional revolver rounds, but some folks, seeing the convenience of loading, put forth the idea of using them with rimmed cartridges like the .38 Special and .357 Magnum. But those rounds are supported by the rim, not the case mouth, so if it was desired to be able to use the revolver without clips, that the cylinder also provide support for the rim. The result was "full moon clips" that fit into a recess in the cylinder while retaining enough full length cylinder to support the cartridge if clips are not used.
So, after a long answer, here is the short one. Moon clips will not work in a standard (no recess, no cut back) revolver cylinder.
Jim