"Ackley Improved" is a wildcat family of cartridges designed by Parker Otto Ackley. The cases feature an increased (40 degree) shoulder angle designed to decrease body taper, which also results in higher case capacity.
The barrels/chambers are different for each caliber so you are not able to interchange the two cartridges. You can fire the standard parent cartridge in an Ackley Improved gun, but the case will then be fire-formed to the Ackley Improved chamber and it will no longer be able to be shot in a standard rifle.
The standard Factory Crimp and Collet Dies for the parent cartridge should work, provided that the base to neck/shoulder intersection dimension has not changed. Most Ackley Improved cartridges have less body taper and a steeper shoulder angle, but the distance from the base of the case to the neck/shoulder intersection has not changed. There is usually enough clearance in the standard Crimp Collet and Sizing Collet to accommodate the Improved cartridge. However the Full Length Sizing Dies and Bullet Seating Dies are not interchangeable and must be made for the appropriate cartridge.
We do offer Die Sets for some Ackley Improved cartridges. To see the calibers we offer, please see the list of our dies here: https://leeprecision.com/reloading-dies/rifle-dies/