It looks like the dragon image was created for a conference paper and I don’t have the model or the commands to replicate it. I will contact the author and see if he still has that.
The sculpt algorithm works by embedding a model in a Cartesian grid and then using a level-set calculation to determine which cells and how much of each cell is inside the model. It then adapts the mesh and adds additional cells to match the boundary as required. The surrounding region shown in the manual represent the Cartesian grid and is fundamental to how the algorithm works.
Regarding the type of adaptive meshing, sculpt does a 1-to-2 element hex refinement along the side. Thus, a single hex face adapts to 4 hex faces through the transition zone. You can see the pattern in the image below.
You can access the adaptive meshing settings in the GUI under the Advanced Settings.
Thank you so much, Karl! Great information!
Initially, I was confused because some of the refinement types were not working for my STL model. Finally, I can see that “Surface to Surface Distance” works for my model.