Who is the real Jason Bourne (in the movie, not the book) PLEASE ANSWER?

In the ending scene of Bourne Supremacy Jason (the fake Jason) starts to remember that infact he volunteered himself to the whole assassination treadstone thing. He remebers killing a person with his gun which signifies his acceptance into treadstone. Was the person he killed the real Jason Bourne? I find this movie more confusing than inception and the books didn't seem very much like the movie ( i read only a summary)