3d – How to implement projectors with perspective projection?

I was reading shadow mapping with directional lights
and noted that the projectors are implemented by rendering with the perspective projection, indicating that the projector worked exactly like the camera. However, I do not see what it could be, because the cross section of a projector is a circle, but the cross section of the projection trunk in perspective is actually a rectangle; will there be no additional information or too little? Or am I missing something. If you have any questions, do not hesitate to ask them. I will try to answer you as soon as possible. Thank you very much for your time!