The gray areas are a variety of non-passenger spaces used for a variety of purposes. Having been on tours or having a drill take us through a few of them, many of them are no where near as "nice" as the passenger space - it is "backstage".
On Deck 3, the big gray area are the kitchens for Luminiere's/Triton and Parrot Cay - there is a great backstage tour that you need to get tickets for on 7 day cruises.
On Deck 4, there is the Kitchen for Animator's Pallette.
On Deck 3 there is a huge backstage area for the Disney Theater. The last time we did a 7 day Eastern, the exit from the US Immigration check in the theater was through this area, ending up in Diversions.
On Deck 2, part of the path to the Ships Infirmary is basically a hallway through gray areas.
On Deck 5 there is a gray area that is actually a connector between the Club and Lab to move kids. My kids have told me that there are stairways that they have used moving from place to place that are not the ones all of the passengers use. I know there is a semi hidden set of stairs from Deck 8 up to deck 9 that comes out behind Topsiders.
There are lots of closets/storage areas around that show up as gray that you see crew moving stuff in and out of - including service elevators that your bags are moved on.