We're Alive REP-ivia!!!

[Osiris]

This is a Fact: Victor was married, wife was like Frodo, he sold insurance.
This is a Story: "Back when I was little, I used to enjoy watching Looney Toons while eating bacon. My older brother, Willie, would tease me, saying that if I kept eating so much bacon that I would someday make noises like a pig. Sometimes he would hold me down and draw cartoon characters on me with a marker. I would cry so hard that when our mother would come into the room my sobs made me stutter. Willie really got a kick out of making me talk like Porky Pig. One day I took a permanent marker and drew all over his face. Boy, did he really loose it." - Duncan Roberts

This is the definition of backstory

Noun

1. A history or background created for a fictional character in a motion picture or television program.
2. Similar background information about a real person or thing that promotes fuller understanding of it.
   

Both of your examples fall into the definition of the word.

Further, your example of story is anecdotal narrative. Is that what you were looking for when you asked the question, or are you just being frustrated by the confusion that it has caused? Anecdotal narrative relates events of the character's past, while backstory tends to provide information that has formative value to the character in question. Why he's afraid of the dark or why he can't go into small spaces. How his father used to beat him, and even though he screamed and cried for her to help, his mother would just close the kitchen door and turn up the radio, which is why he doesn't give a shit that he's dying of lung cancer and is refusing to see him. Also why he doesn't blame his mother; she was going through the same abuse with him.

However, why is he so good at reading people? He was an insurance salesman! You say that it's fact, I say it's backstory. You say his brother drawing on his face is backstory, I say it's a past event and therefore, fact.

If we're going to split hairs . . .