That is the difference indeed. It is much simpler to accumulate random angle values and just stop once you reach 360 that distributing random values to a set number of points so that their angular sum makes exactly 360. Also keep in mind that just assigning random values to the rotation wouldnt work. Its the strict ascending (or descending) order of point “orientations” that prevents folding.
If you apply the second part of my proposition, the number of points becomes random as well (no point in setting it… pun intended 
)
As the shapes will overlap randomly an rbitrary number of new intersection points may be generated…
The number of points could be influenced however by the rotation value range.
For example, if I choose random angles between 36 and 72 deg, the polygon will have no less than 5 and no more than 10 line segments.