The Blind Side is indeed a true story. It tells the inspiring tale of how a young man's life was transformed through the kindness and support of a family. Many of the events and characters are drawn from real life.
It is indeed a real story. The movie depicts events that actually happened to Michael Oher and his journey. However, some artistic liberties might have been taken for cinematic purposes.
The 'blind side story' could be about many things. It might be a story that focuses on the aspects or events that are not easily noticed or are hidden, like the blind side of a character's personality, or an overlooked part of a particular situation.