In both the ZR and R, R means radial. Nearly all passenger tires today are Radial.
Z is the speed rating of the tire. Z rated tires are high performance tires. The Z designation is not important in selecting tire chains. Since ZR high performance tires are usually low profile with minimal body clearance, it is important to check tire chains clearance requirements in your owner's manual to prevent damage to your vehicle.
In other words ZR and R use the same tire chains.