Like the Migration model, the elements in the ring and disc models each hang from two strings.  But unlike the Migration model, the ring and disc elements swing side to side, parallel to the plane of the strings rather than perpendicular.  Perpendicular swinging is the common stable arrangement.    Parallel swinging is unstable, requiring the avoidance of things that initiate perpendicular motion, such as unsymmetrically shaped elements, off-axis starting motion, vibrations in the support structure, and air currents. 
The underlying physics also differs somewhat.  The parallel case (ring and disc models) is a four-bar linkage, with effective pivots at the top and bottom of the strings.  The common perpendicular case has just two effective pivots at the top of the strings.