If you stick card in the ground at noon and make it parallel to sun rays (to cast just thin line shadow), during Earth's rotation it will draw cone.
That is because card will not be perpendicular to Earth's axis.
Except for equinox.
Other side of the cone (at midnight) obviously won't be parallel with sun rays, and if the Earth was transparent then the card would cast shadow on ceiling wider than just line.
Obviously, the angle between sun rays and the card changes during the day.
Again, on days other than equinox.
On the other hand, during equinox, the card will draw flat ring around Earth wherever in the world you set it.
Shadow of the card will remain thin line all day.
Or shadow of blinds.
In FE model card shadow (or blinds shadow) wouldn't remain thin line anywhere in the world, on any day.
Not even at the equator on equinox.
In FE model all latitude ring planes are the same plane, never parallel with sun rays.
In GE model every latitude ring plane is different, but they are all parallel, and all of them are parallel with sun rays for equinoxes.