I note already posting on the rifle crimp dies. They are completely different. They are a collet type die that crimps a rifle case in a ring around the bottom edge of the case mouth like the ones Lake City puts in ball ammo rounds. And yes, they do distort their bullets, but the accuracy requirement for ball ammo is very low by target shooting standards, and bullets staying in place in full auto feed is their primary concern.
The rifle die is called a: Lee Factory crimp Die.
The pistol die is called a: Lee Carbide Factory Crimp Die.
The pistol die, as described, has a carbide cartridge OD sizing ring and an internal ring with the profile of a fairly conventional crimp shoulder. No collets are involved.
If you are reloading 40 S&W, the Lee Carbide Factory Crimp Die plus the Lee accessory Bulge Buster tool may be useful. 40 S&W is famous for developing a bulge in a partially unsupported barrel that is not fully ironed out by a conventional sizing die, so the rounds don't feed well. If you have this situation, the Lee die is put in your press and the crimp ring and its retaining plug are removed and the Bulge Buster accessory forces your cases completely through the OD sizing ring, head and all, to remove the bulge before you start the reloading process. This insures feeding.
If you then also use the Lee CFCD to form your crimp, that's a bonus. You don't have to have a separate crimp die, but most match shooters have reported for years that separately crimped pistol ammunition is a little more accurate. I'm not sure why, but suspect it is mainly about eliminating the very slight shaving of the bullet that can occur when seating and crimping simultaneously. The main thing, as Bart warned, is you have to be sure not to crimp below the minimum SAAMI mouth OD for the case unless you are headspacing on the bullet before the case mouth reaches the end of the chamber.