Why do screws have lower shear strength than nails?
Answering the question asked, without reference to video posted:

Posit a nail and a screw made from exactly the same material.

Observe the shape. One is a smooth cylinder, one has many sharp deformations arranged in a helical manner.

Even if the screw is sized such that the unthreaded core is the same size as the nail (which would make a much larger screw than nail) the sharp discontinuities of the threads concentrate stresses applied perpendicular (in shear) to the axis of the screw, while the smooth surface of the nail does not concentrate those stresses. Google "Stress riser" for more insight...

In short, the shape makes the screw weaker in that direction.