Reflective and narrative essays are two forms of writing that use storytelling as the main vehicle for communicating the ideas and themes of the author. Differentiating between the two modes is difficult because certain narrative essays, such as memoirs, can be considered reflective if they focus specifically on reflection, and a reflective essay can be considered narrative if storytelling is the only technique used. That being said, reflective and narrative essays have fundamental differences.
One significant way in which a narrative and a reflection essay differ is that a reflective essay has a specific purpose: to show how you've made sense out of a particular event -- or series of events -- in your life, and how that experience has shaped the way you look ahead to future events. A narrative essay may have the same purpose, but it doesn't have to. A narrative essay is used to teach, to expose a certain element of the human condition or simply to entertain.
A narrative can afford itself to a wide range of audiences. Some stories are meant for children, others only for adults. Some stories are for general readership and are not meant for any specific audience. A reflective essay, however, is often assigned in an academic setting, so the audience is usually a teacher or committee who will judge your character based upon your essay. For example, the Library Prize for Undergraduate Research at UCLA considers the reflective essay a crucial element in its application packet. A more common form of the reflective essay is the college application essay.
Perspective is the term used to describe who is telling the story. Because the narrator of a reflective essay is always the author, that type of essay will always be told from the limited first-person point of view: the narrator refers to himself or herself as "I." A narrative essay, however, is told from any perspective: first, second or third, or even from a combination of several perspectives.
For either of these forms, structure is a bit tricky to pin down. The way these two types of essay differ in terms of structure is that the reflective essay has an introduction and conclusion that work similarly as in other essay modes: the introduction states or implies the point of the writing, and the conclusion re-states or illustrates it while making one final, interesting point. The narrative doesn't use these two elements, but instead begins with an inciting incident and ends with a resolution that leaves the reader feeling satisfied with the reading experience. Those elements aside, the structure of either form is wide open for all the various methods of storytelling.