Hello wizprod,
Yes, mesh based calculations are providing the area value as a sum of areas for each polygon of the model. DEM-based area measurement gives you 2D area estimation.
The volume calculation of the mesh includes the total volume inside the watertight mesh components. If you are using Close Holes option for making holeless mesh model, which has limited (practically no) control, the based plane cannot be confirmed, like it can be done for DEM based measurements.