The broader term out of the two is "story." Whether it is told orally or in writing, a story might be either true or made up. You can discuss a newspaper article you read, a story your grandma told you when you were child, or another topic. Your grandmother's account of events may not be accurate, despite what the newspaper claims. A story can be written in prose or poetry and typically, but not always, it deals with a number of events that happened in the life of the author.

After seeing the film, he went around telling the story to everyone.

A "tale," in contrast to a "story," is typically made up, the word implies exaggeration. In general, tales focus on thrilling but fictitious occurrences that happened in the distant past. For instance, we discuss the King Arthur and the Round Table legends.