History: Utilizamos history para referirnos a los hechos ocurridos en el pasado, por ejemplo los referidos a un país, ciudad, monumento, también a una historia clínica o a una historia personal. Son hechos reales.
I enjoy reading about the history of World War II.
History shows that the change of government was inevitable.
The history of this town spans four centuries.
Story: Contamos cómo ocurre algo, no tiene por qué ser real. El tiempo al que nos referimos puede ser pasado, presente o futuro.
The film was based on a true story.
His parents didn't believe his story.
The journalist wrote a story for the newspaper.