Well, there are also words like spin a yarn. It has a bit of a folksy or old - fashioned feel to it, often used when someone is telling a long, perhaps somewhat embellished story. Another one could be 'chronicle', which gives the sense of recording a series of events in the form of a story, like when historians chronicle the events of a particular era. And then there's 'recite', which can be used when someone is telling a story from memory, like reciting a folktale that has been passed down through generations.
There are several words. 'Parable' is like a short story that teaches a religious or moral lesson. 'Narrative' can also be used in place of short story in some contexts as it refers to a story or account of events. Additionally, 'mini - saga' is another term for a very short story, often with a specific structure and style.
Some other words for life story could be 'biography', which is a written account of a person's life. Another word is 'autobiography', which is when a person writes their own life story. Also, 'life narrative' can be used.