Colorists work either for recreational or professional purposes. Recreational colorists usually color for one of two reasons: personal enjoyment, or popularity. Coloring gives those who struggle with rendering opportunities to shine in special art communities without doing what they lack in. Consequently, this is often seen as a shortcoming by critics, especially if the original artists of drawings or linearts do not specifically need the assistance of colorists.
Amateur colorists that are respected typically work with complicated lines and styles that do not identically resemble original character appearances. They also focus a lot on drawings that are not fanart; i.e., those that are not based on characters from existing television shows, anime series, books, etc. The exception goes for professional colorists, who usually collaborate with comic/anime/animation pencillers when they cannot otherwise color their own work.
Professional colorists work with whatever they are hired to color.