>> Trying to figure out what is different about the clamp shown on the right.
The difference is in how the tail end of the hose clamp is manufactured.
The clamp type on the left is more common, and has slots stamped all the way through the metal - they are holes that you can see through. The worm gear teeth engage these slots.
The clamp type on the right is different in that the stamping doesn't go all the way through - instead, it forms the metal into ridges. There are no holes, and you can't see through it. The worm gear teeth engage these ridges when you tighten the clamp.
The issue: With the clamp type on the left, what happens is that over time, especially if over-tightened, the rubber hose will begin to squish out through those holes. When you remove the clamp, it will leave a distinct impression of where the clamp had been, and sometimes the rubber will have been damaged. There are also times where the worm gear teeth will slice slightly into the top of the rubber hose through the band. The style on the right aren't always perfectly smooth (some are better than others), but theoretically, they would lessen this distortion of the hose and eliminate the small cuts.
There are lots of other ways around this issue - some worm clamps have an extra strip of smooth metal around the inside which guards the hose from those slots. Then there are T-Bolt hose clamps, the nut-and-bolt strap style, spring clamps, etc. Maytag used some nice hose clamps from the factory (not sure what that style is called off-hand), but later parts kits all substitute the cheaper worm drive clamps.
(re-attaching the original image for reference)
