Actually,
In some circumstances, both.
1-use Cowboy Special cases for their original intention, a short case for light loads (both Black Powder and Smokeless in the revolvers chambered in .45 Colt.
2-Use in Single Action revolver cylinders chambered for .45 Colt AND .45 ACP. The Reason to use in the .45 ACP cylinder is if you want to use a bullet that requires a crimp groove. I prefer the CS case in my 45 ACP cylinder in my convertible Ruger Bisley when using the Lyman 452424 Keith 250 gr bullet.
3-Never use the CS case in a double action .45 ACP revolver (if you need a rimmed case in a double action .45 ACP, you will need an .45 Auto Rim case for proper headspace.
4-Special Circumstances:
Taurus built a .45 ACP revolver that did not have sufficient headspace to allow use of the Auto Rim cases. It utilized an extremely thin spring steel moonclip that fit nothing else. They actually were a nice, lightweight, 4” barreled Trail or Carry gun, but were quite specialized and were counter to everything you see above. HOwever, it just so happened that the .45 CS headspaced perfectly in my Taurus and allowed me to use it like the original 1917 revolvers used the .45 Auto Rim cases.
FWIW
Dale53