What’s the difference among paper, article and essay?
If you do research work, you need to publish the research results in journals. What is your writing called? Paper or article?
If you write something and want to publish it in newspaper, it is not research work, what is it called?
If you are in primary school, your teacher asked you to write a story. What is it called?

Question

What’s the difference among paper, article and essay?
If you do research work, you need to publish the research results in journals. What is your writing called?  Paper or article? 
If you write something and want to publish it in newspaper, it is not research work, what is it called?  
If you are in primary school, your teacher asked you to write a story.  What is it called?

Answer

Popular periodicals are called "magazines" and "newspapers." The pieces in them are called "articles."

Professional scientific periodicals are called "journals." The pieces in them are called "papers."

An "essay" is often a short, nonfiction, literary work. People expect essays to be well-written. People expect essays to be thoughtful and opinionated. Some of the opinion articles in some magazines might be called "essays." For example, "The New Yorker" often publishes essays.

Answer

Short answer

Research - Paper
Newspaper - Article OR Essay (it depends)
Primary School - Composition (usually)

Long answer.. it depends on many things. But safe to say above is generally correct.