I presume the upper image is raw data, the lower being the area after being subjected to a histogram equalization stretch. Or did you use your own image processing software to generate those histograms from a published (and presumably, already stretched, image) and from a published stretch of it?

The upper image shows very few pixels brighter than about 150, the few outliers to the right being the feature of interest. In the lower image, it appears that the range has been mapped to fill the full dynamic range 0-255, so that the lighter areas on the dayward side are now brighter,and the feature of interest appears saturated.

It appears that there are two separate bright spots, but as the processing is applied, they appear to merge into one single area. You can see the individual pixels in these images, and any bleed from one to another will only be exaggerated by the effects of the stretch, as if you were deliberately throwing a telescopic image out of focus. This results from the point spread function of the sensor--i.e., each pixel does not just record the brightness of exactly that one square on the ground it covers, but also includes some brightness information from the surrounding area, and it contributes to the brightness values of the surrounding pixels. Even a point source much smaller than one pixel would bleed into the surrounding pixels. As you map the brightness, it tends to blur the image, the price you pay for increasing the contrast.

Conclusion: not only are the spots real, and brighter than the surrounding area, I think they are much brighter than their surroundings. And there are definitely two of them, that is not an artifact of the processing.