Also note that box modeling and polygon modeling both fall under subdivision modeling. Since either method tends to be followed by Catmull-Clark subdivision. And with a few exceptions with some software that can create edges with variable hardness or use the Doo-Sabin method, the smoothing alogrithm works the same. So as a modeler, regardless of modeling program, you're going to want to understand how edge placement and edge flow works in relation to the subdivision process.

To say that one is better suited to organic and one is suited to mechanical is a bit wrong. The real difference is where the focus is in the approach to modeling. Box modeling has a focus on defining volume. Polygon (face-based) modeling has a focus on directly defining the surface. Once sufficient topography or mass of a model is defined, then the differences between the two subsets of subdiv modeling really blurs since the tools past the beginning work pretty much the same. (Moving a vertex, edge, or face, is moving a vertex, edge ,or face indifferent to how it got there.) A good modeler (in the artist sense of the word) can make organic or mechanical models, it's more about practice and the understanding of the topology behavior than anything to do with the software's starting approach.

NURBS is a whole other can o' worms, but it's already been explained better than I could. And the B in B-splines part is Bezier. A.k.a. the mathematician that is the French-curve guy.

---

Barbequed Pixels?

Your friendly neighborhood Wings3D nut.
Also feel free to browse my freebies at ShareCG.
There might be something worth downloading.