Hi Anh, Ruger does not recommended to use Mark IV magazines in a Mark III gun and vice versa.
The main difference in the Mark III and Mark IV magazines is the base plate. There is 1/4 inch behind the back of the magazines in the Mark III. The Mark IV magazines are flush.
All you have to do is grind off that 1/4 inch and the mags will work in both guns.
Stay safe & have a great day!

ANH, The Mark IV 22/45 magazines will work in the Mark III 22/45 with no problems.
The Mark III 22/45 mags will not work in the Mark IV 22/45 without modification.
You have to modify the Mark III baseplate to work in the Mark IV by trimming the rear end of the plastic base plate.
Then they will work in either gun. Sorry but hope this helps.

Hi ANH and welcome to the community. Yes, they will work as they have the same magazine tube. The floorplates are longer on the Mark IV magazines. Cheers and stay safe!

These magazines are identical except for the wider floorplate on the Mark III magazine. Here's a thread on this very question with more insight.
rimfirecentral.com/threads/mk-iii-mag-fit-mk-iv-22-45.1213865/