There's no reason why the same fridge couldn't be used for both stages of the process, as long as it can get cold enough. There are some who use old inefficient fridges for fermentation only, because the fridge can't actually reach CC temps.
That being said, those who ferment in a chest freezer and use a standard plastic fermenter with tap would have to lift the vessel out of the freezer and place on a higher level in order to keg/bottle. Doing so agitates all that settled crud that would've stayed put had you not moved the vessel at all. Such people could instead move that FV to a CCing fridge, where the height is already optimal for kegging/bottling, without agitating the crud.
I find using a secondary works best in my case, conditions and clears at the same time, the last beer I did was pouring clear out of secondary the following day still at fermenting temperature.Though that could have been because of the balls up with the pressure ferment, put a few million yeast cells to the sword that day.
