The further you go down into the mine, the denser stone gets, which makes it harder to mine. When you get deeper, more expensive ores will appear more often. Layers determine the types of stone/ore you see, while Depth is how far down you are. Layer is based on Depth.
Like stone, ore is sold for coins. However, ore typically takes up less storage and is more valuable per unit.
Chests, unlike ore and stone, reward the player instantly without needing to be sold.