In the left-hand chart, points are joined by Bézier curves whose control points are randomly positioned at the same y-coordinate as the corresponding endpoint, but with x-coordinate chosen between at random the minimum and maximum distance from the control point, controlled by the random control point minimum/maximum inputs.
In the right-hand chart, points are joined by Bézier curves whose control points are all positioned the same distance away from the corresponding end points, controlled by the curvature of the symmetric paths input.