I've been looking into getting newer chains. "Ladder" or "radial" vs "diagonal" or "Z" designs are really independent of the type of material used. The cable-type chains are the ones made of steel cable and little crimped on rollers on the traction portion of the chains. The standard link style chains are of course made of chain links (duh).
The following link is for five different styles of chains: a ladder-type using links, a ladder-type with cable/rollers, a diagonal type with cable/rollers (and a rubber chain tightener), and two diamond-types using links.
Security Chain has several different variations.
I tried and gave up. The strange thing is that the instructions with my cable chains recommend draping them over the top of the tire, then attaching them at the bottom. I tried in my garage and it ain't easy. The hard part seems to be getting the hands around the back. Of course it's supposed to be tightened a bit after driving a few feet. I've got the common Cobra Tire Chain from Quality Chain.
More traditional instructions (I've seen on the web) for the ladder type chains is to lay them down, drive over them, connect the attachments (which are no longer at the bottom), drive a few feet, and tighten. This seems easier for some reason if I don't try and tighten them at the bottom. I would even venture to guess that it would be even easier to do this with the tires jacked up in a garage, before venturing out into the snow. ;-)