Shape and form define objects that are situated in space. The factor that makes the major difference between them is that shape is in plain 2D, while the form is in 3D. Form is usually described by lines, while the shape is defined by the number of sides and amount of angles.
The shape is a well-defined and clear border, while form goes into details of making reference to the area formed by the lines. With this, the shape, which is in plain 2D, has the fundamental dimensions of both length and breadth, while the form, which is of 3D, has a third dimension, which is the height.
Forms simply refer to the 3D that is equivalent to a particular shape. For example, the form of a triangle can be a cone, the form of a square can be a rhombus, and the form of a rectangle can be a cuboid.