One common theme is the battle of ideologies. Bruce Wayne stands for a world of rules and order, while the Joker wants to disrupt it all. Another theme could be redemption, where either character might be on a path to change. Also, the theme of obsession is often present, as the Joker is obsessed with Batman and vice versa.
In 'Bruce Wayne x The Joker Fanfic', their relationship is often complex. It's a clash of two extreme personalities. Bruce Wayne, as Batman, represents order and justice, while the Joker is chaos incarnate. Their interactions can range from intense battles to psychological mind - games. This relationship is what makes many fanfics so interesting as it explores the duality of good and evil in a unique way.
Definitely not. In comic books, Bruce Wayne is Batman and the Joker is his arch-nemesis. They have no familial connection. Their dynamic is based on good versus evil, not kinship.