I don’t know what an essay is like. In our Russian school we didn’t use the word эссе.
We use this word, at least at universities - definitely. Реферат and Эссе are different words, but I don't know how it will be in English.

Реферат - a text about the read by pupil literature, containing an autor's opinion about it with a lot of quotes and references. But there is often taken lightly to this demands and pupils just copy text from the Internet and say that it's a Реферат
Эссе - a free, emotional text of a some problem/theme. There is no structure, no limits, no rules.
Сочинение - a free text about a some problem, but usually there is demands of certain structure of the text, we name this structure a plan (план).

The difference between Эссэ и Сочинение: http://vchemraznica.ru/chem-otlichae...e-i-otlichiya/