The first use of half-moon, now full moon clips was to enable the use of rimless autopistol cartridges in a revolver. The best known is the 1917 .45s from Colt and S&W, the clips a S&W design for use in WW I. There was a Webley-Fosberry automatic revolver in .38 ACP that used a clip, too.
It is possible to clip rimmed revolver cartridges IF the cylinder is altered to accept the thickness of the clips. If that is done RIGHT you can shoot either with or without clips.
Clips do NOT enable you to shoot rimless cartridges in a rimmed chamber like 9mm in a .38 Special unless the chambers are reamed to accept the tapered 9mm cases. That will let the Specials bulge to an alarming but not dangerous degree. I have read of a S&W 686 .357 being rechambered and cut for clips that could shoot 9x23 Win, 9x21 Italian, 9mm P, and .38 Super in clips. It would still shoot .38s and .357s but the brass was too bulged to be reloaded.
That seems like a major sacrifice to shoot crap ammo in your good revolver, but it can be done.
I have READ that it works better to modify a .45 Colt to take clipped .45 ACP and still shoot the LC. Has to be a double action swing out revolver like S&W 25-5 or Ruger Redhawk. You can't get the clips in and out of a single action, those have to have a replacement cylinder.