A true Shaker door is a reversed raised panel. Some of the door manufacturers sell flat panel doors and call them Shaker doors. But there is a difference. When I make them I sometimes backcut the panel so the door is centered in the frame. (Although this also isn't a true Shaker door) Without the backcut, a 3/4" panel will sit proud of the frame unless you sand down the raised panel.
If you're talking historically, PK, then nearly all panels had the back relived a bit where they entered the rail and stile dados. So yes, historically a shaker panel would be "raised" on the back. As would any other door panel (others raised on BOTH sides. However, I haven't seen any cabinet or furniture manufacturer who does that today, so I'm not sure the point applies to the situation.
You can order reversed raised panel doors from most of the door manufacturers.
I used to think that a flat panel door was a Shaker door myself until a furniture conservator explained the difference. I know that a lot of the catalogues will list a flat panel door as Shaker style, but really they're Arts and Crafts. Look at any of the catalogues and you'll see so-called Shaker doors with rope moulding and all sorts of adornments, is this a correct usage of the name?
It may not matter to the majority of people this question of definitions, but it does to some. If you bid a kitchen and specify Shaker doors and show up with flat panel doors you're going to have a problem if the person who's paying the bills knows their furniture.