The difference between polygons and surfaces is this:
A surface is a Nurbs object, which is a Non Uniform Rational B Spline. These objects were the first kinds of objects people in this industry started working with in 3D before the polygon came around. These types of objects are great for creating natural organic meshes because they are smooth objects. (Example: It's better to create an apple from a nurbs surface than a polygon.)
A polygon is an object that is great for creating all kinds of meshes, smooth and non-smooth. They are by far much easier to work with than a nurbs surface and can be smoothed and manipulated in an easier fashion. Essentially, if you create a poly cube, each face of that cube is a polygon. (Example: It's better to create a car out of polygons than to create it out of a nurbs surface.)