It seems like the colors on the right are the "true" colors, but the PNG file contains some sort of "filter" that enhances the saturation but only gets recognised by certain software including Photoshop.
Point is, I'd like to work with Photoshop and see the actual final result, and I'd like to make it so that the result is consistent across different softwares as much as possible (of course different computers or devices are going to change the colors ever so slightly, but when it happens on the same PC, and even in two different views of the same software, there's something going on!).
The above images are screenshots.