The intersection between 2 planes is an infinite line however between a rect and a plane it will be a line of finite length.
Also unless 2 planes are parallel to each other there will always be an intersecting line whereas a rect is much more likely to not intersect with the plane at all.
I would check
1) are all the points of the rect on the same side of the plane in which case they are not intersecting
2) if test 1 above shows the rect is across the plane, create a plane from the rect, calculate the intersect with the other plane and then clip this intersect to the rect's bounds.
Also unless 2 planes are parallel to each other there will always be an intersecting line whereas a rect is much more likely to not intersect with the plane at all.
I would check
1) are all the points of the rect on the same side of the plane in which case they are not intersecting
2) if test 1 above shows the rect is across the plane, create a plane from the rect, calculate the intersect with the other plane and then clip this intersect to the rect's bounds.