“The cast shadow creates an effect just like a splotch of ink that is dropped on a subtly modelled drawing done in delicate halftones. For this reason artists generally eliminate, or soften, cast shadows by toning them down, so that the form beneath can be read.”
— Nathan Cole Hale, Abstraction in Art & Nature, page 17
A cast shadow is the one that “falls on the ground” when the sun or strong light shines. It is more like a dark glaze than a streak of opaque black; we still see a lot in a shadow. Yes we want tonal contrast in a painting for visual interest, a fair distance between the lightest and darkest tones, but tread softly, with colourful dark footprints, don’t stomp shadows in with flat black. A cast shadow isn’t the same throughout either, it gets lighter the further away it is from the object creating (casting) it, and the edges softer (less distinct).
A form shadow is the “dark side of the moon”, the darker tones on the opposite side of an object to where the light’s falling. These are even softer than cast shadows. They are essential for creating the illusion of 3D in a painting or drawing. How much form shadow you see depends on the light direction; if most of the subject is in direct light, there’s very little (unless you walk around to view the other side of it). If you find the thought of two types of shadow confusing, try labelling a form shadow as “lack of light” instead.