Area is 2D area looking down. Surface area is 3D area of surface inside region.
Area is the 2d plane. Surface area is a 3d measurement that includes the elevation changes which is why it is always larger. Basically a 3d surface is a bunch of triangles that connect the points from the point cloud together and a surface area is the sum of all the areas from those individual triangles.
Thanks and apologies for being late in that.
No worries, a quick sketch for future seekers.