Round vs. Flat
Round characters are characters who are complex and realistic; they represent a depth of personality which is imitative of life. They frequently possess both good and bad traits, and they may react unexpectedly or become entangled in their own interior conflicts. These characters have been fully developed by an author, physically, mentally, and emotionally, and are detailed enough to seem real. A round character is usually a main character, and is developed over the course of the story. A flat character is its opposite, having hardly any development whatsoever.
A flat character is distinguished by its lack of a realistic personality. Though the description of a flat character may be detailed and rich in defining characteristics, it falls short of the complexity associated with a round character. A number of stereotypical, or “stock” characters, have developed throughout the history of drama. Some of these characters include the country bumpkin, the con artist, and the city slicker. These characters are often the basis of flat characters. Supporting characters are generally flat, as most minor roles do not require a great deal of complexity.
Dynamic vs. Static
A dynamic character is the one who changes significantly during the course of the story. Changes considered to qualify a character as dynamic include changes in sight or understanding, changes in commitment, and changes in values. Changes in circumstance, even physical circumstance, do not apply unless they result in some change within the character’s self. By definition, the protagonist is nearly always a dynamic character. In coming-of-age stories in particular, the protagonist often undergoes dramatic change, transforming from innocence to experience.
In contrast, a static character does not undergo significant change. A static character is a literary character that remains basically unchanged throughout a work. Whether round or flat, their personalities remain essentially stable throughout the course of the story. This is commonly done with secondary characters in order to let them serve as thematic or plot elements. Supporting characters and major characters other than the protagonist are generally static, though exceptions do occur.
From the blog of Kim Sprecher, English 10. http://www.englishrocks1.net/