Having been somewhat baffled by the contradictory explanations of the clarity slider I have seen in the past, I decided to test my understanding of that and compare it to the new texture slider.
From what I have read and seen, the clarity slider combines at least two different adjustments: midtone contrast and local contrast. It appears to alter saturation as well, which would make sense if it is doing a midtone contrast adjustment on the R, G, and B channels.
From what I have seen, the texture slider is supposed to affect higher frequency details than are affected by the clarity slider, but I found no references to midtone contrast.
So, I created the following set of images, all based on a roughly 100% crop of an otherwise unedited image. First, here is the unedited image:
And here is the corresponding histogram:
Now, here is the same image with texture set to 100, followed by the corresponding histogram:
The details are more visible, while the histogram is only slightly altered. This is what one would expect with a local contrast adjustment.
Now, here is the same image with texture returned to 0 and clarity set to 100:
In this case, the increase in midtone contrast is obvious from both the image and the histogram. There is an increase in saturation as well.
What is less apparent is the other, advertised difference between the two: texture is supposed to affect higher-frequency details than does clarity, if I recall correctly.