Quoted: Michael986255
You would not need to change the barrel. The question is whether your gun is chambered for .32 Colt Long or .32 New Police (.32 S&W Long.) If it is .32 Colt you would need to change the cylinder. If it is .32 New police it will already fire .32 S&W. in the simplest terms if it will chamber .32 S&W you can already shoot them. If not you need to change the cylinder.
This.
Since .32 Colt Long originally used a heel-base bullet the cartridge's outside diameter was the same as the bullet's, like a .22 LR. .32 Colt New Police used the same diameter bullet as .32 Colt Long, but without the heel-base so the casing is larger in diameter so that the full-diameter base of the bullet fits inside.