History are real things that have happened. The history of the USA, the history of El Salvador, the history of soccer,
A story is not necessarily false, it can be real also. I can tell you a story about what happened at my work today, or a story about my childhood in the USA and those are real things. A story can also be a fictional story that someone writes which is a false story meant to be read for pleasure.
Basically history will always be a true thing that has happened in the past, a story can be either true or false.