It's heartbreaking to see the changes....assuming it is the same rug.

YES! this is the "fingerprint" analysis of rugs!

I absolutely think this is the same rug. This carpet had some sort of devastating accident. water for sure, especially with the color run present. The only thing that's going against this is the inside purple color and the border color are the same on the faded rug, but they're different shades on the rich colored rug. The rug is the same size, and same design. My father had a rug just like this. It was a mohtesham kashan silk. The rugs colors were just like the faded one, but when you looked at the back, you could see the colors were true and original. This does happen to these rugs, especially this type of kashan.

Other than design, take a look at the right hand side of each rug, both bow inward on the right hand side.

Take a look at the very, very top right corner of the fringe's kilim. both show similar "scrunching"

it's a little wavy in the same area like there's hard tension in the kilim. It's possible with a silk rug like this, if it had been exposed to water, it would soften, but I cant get a good enough pic of it.

Also see the two lower right hand corners have the same curve upwards, and the lower left corners also both roll back a little.