Paintings and sculptures have different relationships to space.
Abstract painting and sculpture differ primarily in the manner through which they interact with space. Abstract painting almost always maintains a two-dimensional plane, upon which the painting may or may not create the illusion of three dimensions. Abstract sculpture exists within three dimensions, and interacts with space as a dynamic presence within that space, rather than represents space as painting does.
Technique
The technique of abstract painting involves the application of paint to a surface. Abstract sculpture may involve building something up or cutting something away, depending on the technique and style being used. In welded steel sculpture or sculpture made of found objects, the sculpture is created through a process of addition in a manner similar to a painting. In clay, wood or stone, however, the sculpture is what remains after the excess material has been removed. This technique is fundamentally different from the additive technique that is the basis of painting.
Perspective
Perspective involves the interaction of the viewer's eye to the surface of the work. A painting may or may not engage in perspectival illusions. Abstract Expressionism was famous for attempting to escape from the illusion of perspective and present the flat reality of the canvas without attempting to disguise it. Sculpture, because it exists in three dimensions, employs a form of perspective in its very existence, because the viewer's eye will perceive the mass of the sculpture as it exists within space. This creates a primary difference between abstract painting and abstract sculpture. In the first instance, perspective may be absent, or may be introduced voluntarily. In the second instance, perspective is inherent within the work.
Surrounding Space
Paintings and sculptures interact with surrounding space in profoundly different ways. A painting is separated from the space in which it exists by a surrounding frame. Paintings are usually displayed flat against a featureless wall, further reducing the impact of surrounding space. A sculpture is displayed so that viewers can walk around it and see it from all sides, thus necessitating its involvement in the space where it is installed. Whether it is an art gallery or a street scene, the viewer will be more aware of what surrounds a sculpture than of what surrounds a painting.
Concrete Form
Many abstract painters attempt to escape the dominance of form by creating imagery that is mobile and formless. This pursuit is difficult when working in paint, but nearly impossible when working in the realm of sculpture. Because sculpture is by definition form, any attempt to access the realm of the formless through sculpture is bound to fail. The ethereal imagery of formlessness is a quality of painting that sculpture can't access.
