Difference Mesh - Surface

Well you could look at it as meshes are approximations to surfaces. Most interesting surfaces are smoothly curved so you can augment the mesh with further information about the underlying surface (this is what shading normals/tangents attempt to do).

Surfaces could also be described by other things, like parametric patches, or implicit functions (i.e. f(x,y,z) = 0). Meshes tend to be the most flexible and controllable though, plus rendering hardware is optimized for them.

Thanks!

(By the way, DirectX also uses the term "surface" to refer to an "image" or "buffer" type area... don't want to get them confused.)

-M