A shed snakeskin appeared when I opened the garage door:

The skin sits atop the retaining wall next to the door, on a stone(-like) background with poor contrast: even an empty snake has good camouflage!
The exterior looks like genuine snakeskin:

I didn’t know the interior has an entirely different pattern:

As far as I can tell, the snake was going about its business elsewhere in the yard.
To be fair, there’s some luck involved.
Update: After Mitch nudged me, I found the (somewhat the worse for wear) snakeskin again. The head end was split, much as I described, but the tail end was intact (the snake having pulled out like a finger from a glove) and what I though was the inside of the top was the outside of the bottom, just pushed inward to form a very thin double layer.
Today I Learned … to always look closer!
Maybe I don’t understand which part you’re saying has the different pattern, but the skin has the same pattern as the scales on the snake. The wide scales are on the bottom of the snake.
The split seemed to run right up the middle of the bottom, with the interior different from the exterior, but I didn’t do a teardown … which (as usual) means I likely got it wrong.
If it’s still around, I’ll take a closer look and learn something new today!
The post now has an update: you’re absolutely right, of course! [grin]
Thanks …