The splines choices are just different mathematical ways of defining an interpolated curve. Some are smooth and some types hold tighter to given points.

The term spline comes from the flexible wooden devices used by shipbuilders and draftsmen to draw smooth shapes. Incidentally, these devices were often used in the lofts of large barns to trace these curves onto shipbuilder's full-scale drawings, thus the phrase "lofting a curve."

Shown here is a diagram illustrating BobCAD-CAM V21's different ways of producing these curves: