GC refers to two translations that need to take place to give each element what it needs.  the render deals with linear math.  sRGB inputs, like images and colors picked on your screen, are gibberish to it.  the screen works in sRGB.  linear input is gibberish to it.  if you correct in Photoshop, you can only deal with what the screen gets, because the renderer has already received and processed gibberish (as understood by it). 

in terms of results, when you render without linearizing your input, our brights come out too bright and your darks are too dark. you've lost any information above white and below black. even within that spectrum, there are ranges that have become single colors.  in the calculations, you have as many levels of value as the accuracy of renderer allows, but in the render you have only 256 values from black to white in any one color. 

to be succinct, even if you linearized your input, you've lost information just by going to an image that isn't a raw format.  Photoshop can't return that information to your image.