Data Set Dimensionality

Type of data 2D 2.5D 3D
Vector Shapefile Most Shapefiles are 2D, with only the horizontal coordinates   The shapfile specification allows a z coordinate to be stored for every point.  Few data sets use this option.
DEMs or grids   A grid can only have a single value at a point, so it is not truly 3D.  The grid cannot store caves, overhanging cliffs, or features above the ground.  Having both a DTM  and a DSM is one way around this limitation with gridded data.  The conforms to the mathematical concept of a single valued function:  if the earth's surface elevation z = f(x,y), or z = f(Lat,Long), there can only be one z value at a point.  
Point clouds     The point cloud can show the full 3D nature of the data.  There can be multiple elevations at the same point, or close to the same point, subject to measurement uncertainty.  Most of the multiple points will be features above the ground, like vegetation or power lines, but they can include overhanging cliffs or caves.

If you have complex man made features like buildings, with the interior, you will have multiple surfaces and a true 3D data set.

Last revision 3/22/2016