I think Kate's toy plane is different. It had two broken propellers on it, and a sticker with the number (I think) 5025. I remember the number because at that point, I was searching madly for every number I could find in the show. Her old boyfriend supposedly got the plane when he went on his first airplane flight, a flight to Dallas. We know the plane is important to Kate because she associates it with her first love, the "Man I loved, the Man I killed" but what else it might mean is a mystery.