Pi, in the animal story, represents his more humane, decent, polite, religious, polite and controlled self. Richard Parker, in the animal story, also represents Pi, just his more barbaric, animalistic self that does all of the difficult things that enable him to survive. Pi is thrust into a very difficult situation, where he is forced to do things that are extremely uncomfortable for him, and even abhorrent, in order to survive. He is normally an educated, respectful, vegetarian boy who would never hurt anyone or anything. However, if that part of himself reigns, he would die quickly on the ocean. So, he gives in to his more animalistic side in order to survive. He lets that side take over to kill, take control, be dominant, fight the odds, and survive the tragedies.
Often, in stressful situations, people have to do things they never would have imagined themselves doing. Pi does that here, and embodies all of those horrific acts in the animal of Richard Parker, a fierce tiger in whose nature it is natural to fight and kill. Pi separates himself from the horrible things he does by putting them outside of his normal self. So Pi, in the animal story still represents himself, just the human, humane, decent part of himself, the part that would never do horrible things or hurt others. He has to maintain that part on himself in order to remain sane, and to keep a semblance of his old nature. So both Pi and Richard Parker, in the animal story, represent Pi, just different parts of his nature that, in order to survive, work together. I hope that those thoughts helped a bit; good luck!