The word should be spelled "essay," with two s's and one a. 

There's no clear difference. The meanings overlap.

"Composition" can be a non-countable word meaning the act of writing. It means putting words and sentences together. In the United States, people beginning their university studies are often required to take a course in "English composition," meaning "writing skillfully."

A composition means a piece of writing that is carefully put together. 

"Composition" suggests ordinary good workmanship. It suggests competence. Any university student ought to be able to write a good composition. Compositions include all kinds of writing. A business report is a composition. A newspaper story is a composition.

An "essay" is a literary form, like a poem, a play, or a story. 

"Essay" usually means a composition that presents the writer's opinion. So, a business report is not an essay, and a newspaper story is not an essay. It suggests writing that is not just competent, but good. 

I think the Portuguese word ensaio is probably a good translation of "essay." (The reason I think so is that if I look up https://pt.wikipedia.org/wiki/Ensaio_(literatura) , The list of "Ensaístas famosos" contains the names of authors I recognize as English-speaking authors of essays.)