See below for large view of the type of cleat I have. They are called LOOk Kéo cleats according to the Performance Bike website.

When I got my new bike I put pedals on them and they came with a set of cleats. Perfect! To date I have been using the old cleats I had on my shoe. The time came to replace them so I did and when I went to try them out the left cleat snapped in like expected (after some adjustment on the pedal) but the right one did not. I kept thinking the pedal was too tight so I loosened and loosened but come to find out there were way TOO LOOSE and I had to tighten and tighten until I was all the way tight. Now my cleat snaps in but is a bit sloppy. I checked and sure enough the adjustment "thing" is all the way in (from what I know).

I don't understand why the left is just as I expect and the right is not. The cleats looked to be mirrors of each other when I was holding them against each other. My old cleats fit as one would expect.

Again the new cleats are the ones that came with the pedal.

Any thoughts?