There are three basic classifications of art: representational, abstract, and nonobjective. These classifications describe how the subject matter is being depicted, or if any subject is being depicted at all.
Representational Art
Representational art depicts subject matter we can easily identify - objects, people, animals, buildings, landscapes, etc. The artwork is a clear representation of something.
Not all representational art is what we would call realistic, but all realistic art is representational.
Although the style of these works varies, all of the works below are examples of representational art.
Abstract Art
Abstract art references real subjects, but it presents them in a manner that is less readily identifiable. To abstract something means to separate or remove, so we can think of abstract art as a depiction of an object, person, landscape, etc, where the shapes and forms have been simplified or distorted.
There are artworks that are slightly abstracted, and there are artworks that are extremely abstracted. In the latter case, titles can sometimes help us determine that a work is abstract. For example, the first example below is titled Bottle of Rum and Newspaper. You may not immediately see a bottle of rum and a newspaper, but we know that is the subject through the title. Make sure you read the titles of each of the examples below.
Nonobjective Art
Nonobjective art is often incorrectly labeled as abstract art. Nonobjective art does not depict any actual objects, people, places, etc. It is entirely about the visual form - lines, shapes, color, materials, brushstrokes, textures, etc. It is not a depiction of any tangible thing, although it may embody intangible ideas like emotions.
This form of art is sometimes also referred to as nonrepresentational because there is no subject matter being represented.
All of the examples below are nonobjective.
Nancy Manter, Transmission,1997, lithograph, source, and Sonia Delaunay, Electric Prisms, 1913, oil on canvas, source