Students are likely to come across both research and persuasive essays during their school career. Understanding the differences between the two styles of writing, and what is being asked of them when assigned these essays, greatly improves their chances of success. Research essays and papers are centered on facts, while a persuasive essay is asking the students to be just that, persuasive about a theory or idea -- although they are expected to use facts to support their point of view.
As the title suggests, researching a topic is the basis for a research essay. Like all essays, an idea (often called an argument) is important in giving the essay its structure, but what is most important are the facts and figures that are found by the writer, which are presented in the essay.
If a persuasive essay is assigned in an English lesson, then it is the ability to use language to persuade and the ability to argue a point of view that is being assessed, rather than the ability to analyze facts and figures. A persuasive essay is expected to demonstrate knowledge and facts about a topic, but to present this knowledge in the form of an argument for a particular point of view. The student is expected to provide facts that back up her point of view, and outside of English, it is the student's ability to find such facts and use them to support her viewpoint that is being assessed.
A science teacher or lecturer is unlikely to give pupils a persuasive essay. The fact that chlorophyll makes plants green does not require a persuasive stance, or a moral point of view. Being able to prove that chlorophyll does indeed make plants green by explaining the results of experiments, researching exactly how this is known and what the process is would be a research essay. Being able to explain those findings clearly and concisely makes the basis of a good research essay.
All essays need to be about something to explain a view or a topic. Having a point to explain, known as an argument, gives essays focus and structure. Writing about Shakespeare is so vague -- it could (and has) filled many shelves of books. Writing about Shakespeare's treatment of women in Hamlet narrows the topic and ideas down to a more manageable size. Giving that topic an argument -- Shakespeare portrays women as weak and feeble in Hamlet, for example -- makes the essay much easier to write and to read.
In both cases, research and persuasive, the argument might have a different viewpoint; there might be scholars who suggest a different process for chlorophyll production, or argue that Shakespeare is reasonable in his portrayals of women in Hamlet. These are always worth mentioning if you can argue against or refute the opposing idea.