The Dark Knight of the planet "Zur-En-Arrh" teleported Earth's Batman to his native planet to help ward off invading robots. This alien incarnation of Batman had many Superman-like powers, due to "unique" elements on Zur-En-Arrh.
The modern version was a second personality created by Batman in the event of a psychological attack. The Batman of Zur-En-Arrh was a much more violent persona of Batman, using bats, pipes and homemade explosives as well as carrying the Bat-Radia. An homage to the original story, this Bat-Radia allowed Batman to control the security systems of Arkham Asylum... And According to Batman: RIP, Doctor Simon Hurt planted a post-hypnotic trigger in Batman's head years before, that is set off by the phrase "Zur-En-Arrh", and that the Dark Knight of Zur-En-Arrh himself was an accidental creation of Bruce Wayne he unintentionally made during a hallucinogenic break-down caused by one of Professor Milo's toxins, that also drove Milo himself criminally insane.
In Batman: The Brave and The Bold, the Silver Age version of the Zur-En-Arrh's Dark Knight (Voiced By Kevin Conroy) meets the Earth Batman, who gains new superpowers (due to a mysterious element) and saves him when Ruthol discovered his weakness, along with the Green Arrow who tagged along as back-up. This version was something of a Superman and Batman mix, And was often referred to as "Super-Bat".