Students of all ages and education levels are asked to write essays, but those essays probably wouldn't sell very well in a bookstore. Writing an autobiography requires that a writer have at least some interesting experiences to recount, and it usually takes longer than the amount of time spent in elementary school to amass enough interesting experiences to create a bestselling autobiography.
There are four traditional types of essays and only one is autobiographical. Persuasive essays argue a point and try to convince readers to agree. Expository essays provide factual information without a writer's analysis of those facts included. Descriptive essays are used to describe an event or other topic. Only narrative essays are written about personal experiences in order to tell a story in the same way an autobiography does.
Narrative essays, like the other forms, include an introduction paragraph, a body of three or more paragraphs, and a conclusion. Also like all other essays, a narrative essay is a short and informative piece of writing. No other common type of essay, however, is told in story form.
An autobiography is the story of a person's life, or at least some part of a person's life, written by the person themselves. While it doesn't have to be comprehensive, beginning on the day the subject was born and ending on the day the writer finished writing, it is an account of a person's experiences over some period of time.
While any personal story told by the person who experienced that story can be autobiographical, a typical autobiography is much longer than the average essay. Autobiographical books are usually written by celebrities, politicians, and people connected to historical events.
While any narrative told in story form by the person who lived the experience being described is autobiographical, essays have a specific structure while many autobiographies exist that do not conform to the introduction/short body/conclusion structure.
An autobiography can begin in the middle of a story and be fleshed out throughout flashbacks of prior times and experiences from the writer's perspective. They can go off in many directions and tell the stories of many different types of experiences, as well. An essay, even a narrative essay, is typically more focused with organized thoughts that make a specific point.
If you have an interesting story to tell, you can write an autobiographical story. Whether that story will be part of a larger autobiography of your life depends on how long the story you want to tell will be.