I think it's largely part of terminology, and too often deep litter and deep bedding are used interchangeably.
My understanding is that deep litter is an active composting system, usually with deep material placed on soil, is moist, and is actively composting in place. You mention that your deep material is sitting on a wooden floor, but the bottom layer is moist and looks like your compost outside. Where are you getting all that moisture? Chicken poo contains urine, but in a deep material setup, it usually dries out fast. If you are indeed creating compost in your setup, then I would lean towards a deep litter system.
I have a dry deep bedding setup in my coop, which does not actively compost. I use wood chips, or last winter I use paper shreds, as my coop litter. I have a wood floor covered with linoleum. My goal was to keep the coop as dry as possible in our long winters. The only moisture in my coop is from chicken poo with urine, and mostly it dries up and works itself down to the lowest layers. Even after a full winter, my litter has not composted much, but the lowest layer can be a bit moist and smelly from the poo at that base layer. I toss all my chicken coop bedding out into the chicken run to begin composting with natural rainfall.
Deep bedding is not specific to wood. Some people use straw, hemp, leaves, dried grass, etc... and last year I used paper shreds. Whatever material you use, it's just dumped in the coop to a deep level. I might start out with 3-4 inches in the fall, adding fresh material on top of the old material all winter, and might have as much as 12 inches come spring clean out. Since I don't encourage active composting in my chicken coop, I call it a deep bedding setup, or sometimes a dry deep bedding system.
Also, you mentioned that your bottom layer of litter did not smell and that it looked like compost. Maybe it is. In my deep bedding system, the chicken poo filters its way down to the bottom, and the bottom layer smells like chicken poo and does not resemble compost. Because I have a number of layers of litter above that lowest base layer, my chicken coop does not smell, either. However, when I clean out the coop, that lowest layer does smell like bad chicken poo accumulated over the winter. But I would in no way confuse it with sweet smelling compost that I make out in the chicken run. Totally different.
