In modern English they are almost completely different. English-speakers almost forget that the words have a common origin. In their most common meaning: A "story" is a tale, a fable, an entertaining account. "The Story of Ferdinand" is a children's book about a bull who likes to smell flowers. I am an admirer of Jack London's short stories. I'm always telling my friends stories about the cute things my grandsons do. A "history" is a serious factual account of past events. "In high school we study geography and history." "'The River of Doubt: Theodore Roosevelt's Darkest Journey' is an interesting book about a curious event in history."

http://www.thefreedictionary.com/history http://www.thefreedictionary.com/story