The theatrical version of a movie is the one that was originally shown in theaters. Thus it is the cut of the movie that the studio thought would be best for the most moviegoers.
An extended version or uncut version has scenes added that were filmed but cut out of the theatrical version. Most often, it is created to entice people have already been to the movie to purchase a DVD since it will contain something extra that they haven't already seen. Since scenes are often deleted because they slow the pace of a film or are redundant, the extended version may be a longer but less impressive experience. On the other hand, the extra scenes may have been omitted to preserve the film's rating; in this case, the longer version may involve significantly more violence or sexuality. Such a version may also be called an international or European version.
A director's cut is often nothing more than an extended version, created to sell more DVDs. However, there are instances in which the director had a vision for the film which was significantly different than the studio's, in which case the director's cut may leave out some scenes from the theatrical version, reorder scenes or have other changes. A well-known example is the director's cut of Blade Runner, in which the voice-over narration is omitted and the ending is different.
A special edition or remastered version of a film is typically a version of an older film created using newer technologies to enhance picture or sound quality or to improve special effects. Other changes can be made as well; a notorious example is the special editions of the original Star Wars trilogy ("Han shot first").