There are many different types of essays, from descriptive and narrative essays to definition and literary essays. Two types of essays that often get confused are the persuasive essay and the argumentative essay.
Both types of essays have at their heart a potentially divisive or engaging premise or thesis that clearly has two (or more) distinct viewpoints and sides. Both types typically begin with a statement of this thesis, one that shows the author's stance going into the essay, and both are designed to impact the reader and attempt to at the very least sway them to consider the writer's point of view. However, this is where the similarities end.
A persuasive essay is designed to draw the reader to the author's point of view. In a persuasive essay, the author only presents one side of the premise, that which they are defending, leaving the other aspect alone. The essay is designed to inform and convince in a fairly passive manner, without introducing conflict or highlighting the possible negatives of the opposite view. The goal is to woo and win over the reader by the explanation and the extolling of the merits of the author's premise, without exploring the other side of the issue at all.
Conversely, in an argumentative essay, the author not only writes about the positive aspects of their topic or view, they also inform on the opposing view, presenting both sides of the issue. The essay revolves around an objective thesis. The manner in which the author informs on the topic may involve pointing out the shortcomings of the flip side of their premise. With a much stronger tone and usually with more points to be made both for the writer's point of view and against the opposing perspective, argumentative essays are designed to convince the reader in a much more determined manner. All claims should be supported with facts and statistics in order to be able to counter or refute the reader's objections.
The end result of a persuasive essay is to have educated the reader and hopefully swayed them to consider your point of view. In an argumentative essay, the intent is also to educate the reader, and to have, if not swayed them, then convinced them to look at both sides.