The terminator is the area where light and shadow separate on a form. Sharp or soft terminators depend on the form itself. For example, a sphere will have a soft terminator because it has multiple planes that travel all around the form. In contrast, a cube has planes which sharply turn at 90 degrees on each side. Think of a cone as well. The flat part at the bottom has a sharp plane change versus the smooth nature of the part of the cone that goes up to its point. There are multiple factors which would determine how the terminator is displayed, however. 1.) The angle of each plane in a form (sphere vs cube). More and more planes = smoother and smoother form. 2.) The positioning and distance of the light source 3.) Hard versus soft lighting 4.) If you have a complex form or multiple forms that project onto another form nearby.

I just found this article where the author used "Form Shadow" but with apparently a different meaning: https://www.muddycolors.com/2023/11/core-shadows-and-form-shadows/ Would you say that what he calls form shadows is actually ambient occlusion?