A form is a conceptual reference to a three-dimensional unit. A form has height, width, and depth and is defined by points, lines, and planes. In a two-dimensional application, a form is an illusion created through the use of depth cues. In a three-dimensional application, a form actually exists.
Form differs from shape. A shape can refer to a three-dimensional unit but it can also refer to a two-dimensional unit. Form always refers to a three-dimensional unit.
Alternate terms: object, volume
Three depictions of form.
Though similar, these two units are not form because they do not depict a three-dimensional unit.
(They are still shapes, however.)