Question: The answer is not given in the film, but does it explain in the early scripts why Jack shot his parents but not Bruce? If not, what was Joe Chill's reason for shooting Thomas Wayne in Batman Begins?
Answer: It's unlikely there was anything in the script addressing this. In the Batman universe and the various interpretations, there's never been one definitive explanation. In the original lore, Bruce Wayne's parents were the victims of a random mugging by Joe Chill, who, for whatever reason, murdered the Waynes, probably unintentionally. Maybe he was startled or Mr. Wayne attempted to subdue him. He may have been mentally unstable and acted impulsively. Bruce was probably spared because many hesitate to kill a child. Chill may have considered Bruce too young to remember specific details. Something could have scared him off. However, this really has to be seen through the lens of a writer. The plot requires that Bruce survive the ordeal in order to grow up and become Batman. His parents' murders shaped and motivated everything in his life from that point on. Otherwise, there would be no story to tell.
Answer: With regards to Chill in Batman Begins, Thomas Wayne is shown reaching towards Chill when he grabs Martha to get her jewelry. Chill gets spooked and shoots Thomas. He then shoots Martha and runs off. Joe Chill is shown to be extremely nervous and on edge, and he doesn't appear to regard Bruce in any way at all; all he wants is the jewelry.
Answer: There's a fan theory that Bruce Wayne projects his parents' killer onto all his enemies, so whoever he's fighting at that particular moment killed his parents.
Answer: Actually, it is answered in the film. Jack did want to kill young Bruce because Jack had pointed his gun at him. When Jack's accomplice begged Jack to just leave the area, Jack walked away.