Form is the envelope or massing of an object or element. The form describes the spatial or volumetric qualities of an object. Form does not have to relate to how it is made, but the form does evoke possible frameworks.
Structure is the configuration of elements or members, creating an integral whole. The structure defines not only how the object appears, but how it holds its shape. Furthermore, structure yields the functional output of an object.
Both form and structure define dimensional constructions that have spatial characteristics, such as mass, volume and center of gravity. In addition, some purpose, whether functional, representational or stylistic, affords both form and structure -- neither is made in a vacuum, without context.
Every structure must have form, and every form must have structure. The structure's relationship to form is similar to the famous Modernist quote by Louis Sullivan that "Form follows function," where a structure's form is defined by its makeup. For example, a tent cannot be a tent without a tensile skin and compressive poles or bents.
On the other hand, form's relationship to structure is subjective, and the shape of the object is not determined by its assembly. For example, a chair will be a chair whether it is constructed of wood, steel or cardboard.