The two main geometry languages used today in 3D modeling are “Polygons” and “Surfaces/Solids”. It’s common for any beginning 3D artist or designer to get confused by where to use each of these two different representations of geometry. I’ll try here to explain it as simply as possible by starting with a comparison of some well known design tools.
Adobe Photoshop and Adobe Illustrator can both be used for making art and graphics but they have vastly different strengths. Photoshop is a rastor based program which means it works with pixels or small square blocks of color. If you paint an image or edit a photo in Photoshop and then realize that it prints far smaller than you intended, you may try to enlarge it. The artwork, since it is pixel based, will lose resolution when scaled up. Illustrator in contrast is a vector based program and the artwork created in it can be scaled up without a loss of resolution. This is because the line work and any color is based on math and not pixels.
This same separation of rastor and vector exists in the 3D world as well. Surface based programs such as Rhino, SolidWorks, ProE, UG, Catia, Alias etc. are like Illustrator in that the content created is scalable without loss of resolution. Polygonal modelers like 3ds Max, Maya, Blender, Zbrush and more will require subdivision if scaled up in order to be smooth.
The image below of a torus modeled as a surface shows the same perfectly smooth geometry at two different scales. The radius dimension of the cross section circle for each is shown. Surface geometry is synonymous with “NURBS” or Non-Uniform Rational B-Splines.
A torus modeled from polygons will only be as smooth as the number of polys used to describe it. To scale the polygonal torus will result in a larger version of each polygon or flat face seen.
Polygonal modelers therefore have “subdivision levels” of detail to allow for each flat facet in the polygonal structure to be split into additional faces. This allows for a smoothing effect but the underlying geometry will still be comprised of flat polygons… just smaller ones.
3D modeling programs will often support both geometry languages but it is usually the case that they are better at modeling with or more well known for one type. Poly modeling is mostly used in film and games while NURBS is the language of engineering and manufacturing.