In that video there is about 4 different shades of light on the white screen. He starts off with the globe close to the screen(and looks like only one shade), but not in the center. But then moves the globe up to the center of the screen where theres a different shade of light on the screen. See how bright the center is. That’s a different light source than the rest of the screen. And it looks like it becomes distorted.
You are literally describing what he is demonstrating.
With a point light source the shadow will always be as big if not bigger than the object casting the shadow.
With an extended light source - like the sun - if the object which the shadow is cast of is far from the surface it's casting the shadow on to then you get a small umbra (in a solar eclipse that's the total eclipse) and a larger more diffuse penumbra (partial eclipse).
The video demonstrates this.
Obviously the size of the umbra and penumbra depends on the relative distances of the light source, object and surface the shadow is cast onto..