You have to delve into some aspects of Hinduism to fully understand Neo's character. I'm not completely literate in this area of discussion, so I will just try to explain the basics. The Neo from Parts I & II is the sixth version. He represents genuine human beings, in that he disobeyed and left "the Garden" (the Matrix) which was a heaven-like environment that the Machines (in their "Creator" role) designed for the humans to live in.
However, at the end of Part II, Neo slips into a coma, and remember that this is shortly after he disobeys the Architect and chooses the door back to Trinity. That's good old "Neo 6.0" doing what he does best, disobeying. This coma is meant to symbolize death for Neo 6.0. The Neo we have been riding alongside for the first two movies is dead; he never makes it past the train station. The Neo we see in Part III is an entirely new version, the one who will bring man and God back together.
Before we go any further, let's clear up some symbols here:
1. The Mobil train station is limbo, the place where purified souls go to await the ascension of Christ back into Heaven. It is the river Styx. The boat is replaced by a train, and Charon the boatman is replaced by the Trainman.
2. The Christ figure has split into man and God when Neo becomes comatose. Neo (man) has gone to Limbo, while Trinity (God) has gone to hell to save him.
3. Obviously, the Merovingian is Hades, Lucifer, Satan, whatever you want to call him. He was cast out of the Machine City and is forced to live in a hell of sorts. You see, to the Machines, the Matrix is hell. Trinity goes to hell to bargain with the Devil, and ends up succeeding by playing him at his own game. She then ends up coming back and reuniting with Neo to take him out of Limbo and begin his ascension. We know the train goes between the Machine City and the Matrix (heaven and hell), and this shows that Neo will have to go to the Machine City if he is to ascend to heaven and unite with God.
I know this sounds confusing, and believe me it is even more confusing to try to explain. I'm sorry for that, but every time I try to decipher one mystery of the trilogy, three new mysteries pop up and I need to deal with them first.
Sati literally means "self-immolation," or a Hindu woman's right to sacrifice herself by burning should her husband die. Sati represents what Neo will have to do if he wants to ascend. He will have to sacrifice himself.
The first thing Sati says to Neo - indeed, the first thing that happens to Neo at all in Part III - is she says "Good Morning." This is blatant. Welcome to a new day, Neo. You are a new person. Good morning.
She asks him if he is lost. Obviously he is, because he doesn't know where he is and did not get there intentionally. Later, the Oracle explains that he tried to touch the Source (unite with God) too early, that he wasn't ready for it. Neo 6.0 was never meant to attempt the ascension, as he was immature and unprepared. But Neo 7.0 will be the one who succeeds.
Neo says to Rama-Kandra (the father of the family), "I know you." ON the surface, this means Neo remembers seeing him in the Merovingian's restaurant. But symbolically, Neo is recognizing himself, he is loking into a mirror. Rama-Kandra is the seventh incarnation of Neo. He will take the torch and the two souls will switch bodies (which is why Neo 7.0 still looks the same as Neo 6.0).
In the Hindu religion, Christ is called Vishnu, and there are 7 incarnations of him. The sixth is called Parashurama, or the Serpent. Neo is dressed in black, and represents the Serpent as I said before. The seventh incarnation of Vishnu, effectively the Christ figure who will bring man back to God, is named - and I am not making this up - Ramachandra. In the Hindu stories about Vishnu, Parashurama and Ramachandra actually meet, and the torch is passed from one to the other. Here we see the same thing. Rama-Kandra's wife Kamala represents another Hindu God, but I don't remember the name. Regardless, we can examine the whole family as one huge in-your-face message: Self-Sacrifice is the child of Divinity. Neo knows what he must do to succeed.
When Rama-Kandra speaks to Neo, he holds Sati in front of him, between the two men. Again, this is blatant. Remember Neo's question from Part II ("I just wish I knew what I'm supposed to do"). The answer for Neo is quite literally right in front of him.
When the new Neo comes out of the train station after being rescued by Trinity, he is now the seventh incarnation, the final version who must sacrifice himself to complete his mission.
Here's a difficult concept to understand: the idea of a divine enlightened being. Neo is forever moving towards enlightenment, but we must understand that to be an enlightened soul means one must possess the ability to make a decision that has no reason or purpose. It must be made completely outside the realm of any influence whatsoever. The decision is the beginning and the end, requiring no answer or explanation. Think of when Smith simply cannot understand why Neo doesn't just give up when they both know he is going to lose. Neo replies with the perfect answer from a wholly enlightened being: "Because I choose to."
Anyway, let's get back to Neo. When he is in the car after leaving the train station, the following exchange occurs:
MORPHEUS - Are you ready for us?
LINK - Almost, sir. They got some pretty ancient hacks here, we're working on it. Did you find Neo?
MORPHEUS - Can't you see him?
LINK - No, sir. We were reading something but I couldn't tell what it was.
Just more proof that this Neo is different entirely from the other one. He may look the same to Morpheus and Trinity, but he is clearly different inside, which can be seen when Link reads the Matrix code and deciphers it.