If you're writing an essay, you're most likely a student, a scholar, or a writer. If you're writing a memoir, you've experienced a significant event and you want to tell the story of it in your own voice and from your own perspective. Some essays fit the definition of a memoir, but not all memoirs fit the definition of an essay.
An essay is a short, informative piece of writing. Essays are usually five or more paragraphs long with an introductory paragraph, a body of at least three paragraphs, and a conclusion paragraph. Essays are written on all kinds of topics, from science to history to literature.
There are four basic types of essays: persuasive, descriptive, expository, and narrative. A narrative essay told from the writer's first-person point of view would be considered a short memoir.
A memoir is an accounting of an event or time period told by a person with first-hand experience or from sources close to those who do. In this way, it is a very similar type of writing as an autobiography.
Memoirs are sometimes autobiographical, which means that they are written by people telling their own story. However, memoirs are different than an actual autobiography in that they cover only a particular time period instead of discussing the writer's life overall. Published autobiographies are usually written by historical figures and famous people, but very popular memoirs have been written by people about their travels, their experiences during war, and the ways in which they overcame certain hardships.
A memoir is usually structured using a timeline of events. Like any essay, a memoir is likely to include an introduction, a body of writing, and a conclusion. The conclusion in a memoir is most often a reflection on the writer's experience with the benefit of hindsight as well as some discussion on the writer's life since the time period the memoirs covers ended.
If you want to research and write a short paper on the first moon landing, an expository or descriptive essay will be fine. If you want to write a narrative, first-person essay about watching the first moon landing on television as it happened, you need to have been alive and tuned in on July 20, 1969. If you want to write a memoir about experiencing that event yourself, your name should be Neil Armstrong or Buzz Aldrin.