In case you're confused about who was Ra's in the film, lemme give you the basics of it. The asian man you meet early on, who is introduced as Ra's al Ghul and played by actor Ken Watanabe, is actually a body guard to the real Ra's al Ghul. The true Ra's uses the alias Ducard for most of the film, and is played by Liam Neeson. The asian man we meet at the party, who is introduced to Bruce by one of his guests as Ra's al Ghul, is the new bodyguard to the real Ra's. He takes the place of the one who died as the new decoy Ra's. In truth, "Ducard", the man played by Liam Neeson, was Ra's al Ghul the whole time. He didn't inherit the title after the Watanabe character's death, or anything like that. Basically, think Star Wars Episode I, with the whole Padme/Amidala thing. It's practically the same thing.
Just thought i'd clear that up in case you, or anyone reading this thread was confused, as it seems a lot of people are.
Now, as to how film Ra's differentiates between comic Ra's. The main difference is how he met Batman. In Begins, he was heavily involved in his creation, whereas in the comics, the two did not meet until well in Batman's career. Ra's sought out Batman as an heir to his empire, the League of Assassins (called League of Shadows in the film) and as a suitor to his daughter Talia. As for appearance, he looked much more like Liam Neeson than Ken Watanabe, although he appeared to be of some middle-eastern decent. He had a right-hand man, and bodyguard named Ubu, who is presumably who the Watanabe character actually is. Also, Ra's al Ghul in the comics is practically immortal, and is suspected to be over 600 years old. He has access to large pits of some sort of liquid, called Lazaraus Pits, and upon entering these his wounds are healed and he regains some youth. They also make him temporarily insane, although they most likely have had some permanent effect on him, seeing as how he's, you know, insane. The neat thing about the film is that although Lazarus Pits aren't mentioned at all, there's nothing to suggest they dont exist. It's perfectly plausible to assume that Lazarus Pits to exist in the film, and the same goes for them not existing. Good writing on Nolan and Goyers part if you ask me, leave it up to the imagination of the viewer, or just wait until a future sequel to decide whether to bring him back.
Also, there was a character in the comics named Henri Ducard, who did have a hand in Bruce's creation. He trained him in the detective arts in France, and he was never connected to Ra's al Ghul in any way that I know of. And while Bruce never trained with Ra's and his League like he did in the film, the training he went through there is very reminiscint of training he went through in the comics with Master Kirigi. Basically, think Pei Mei from Kill Bill Vol. 2, only not as mean. The makers of the film pretty much took that training, combined it with his training with Ducard, and used Ra's instead of Kirigi. Worked out well and made for an interesting story if you ask me.