A cubic spline is made of piecewise third-order polynomials, with continuity, and interpolates each of the points it is created from. The second derivative of the spline at the endpoints is set to 0.
A Bézier spline interpolates only the endpoints. The other points control the spline, forming a convex hull. Given n points, a spline of degree is created.
A composite Bézier spline is made up of a series of third-order Bézier curves with continuity. It alternates interpolating points and control points.
In a composite Bézier spline generated from an even number of points the last two points are reversed so that the final point is interpolated and the next to last is a control point for the final segment; if the spline is generated from an odd number of points, then the final vertex is doubled.