I have come across this term at many places in graduate admissions, and I do not understand it.
For example, here, they want a writing sample that is "a recent scholarly or critical paper, 15 to 25 pages in length." And they do not explain more - which means they assume it is common knowledge what this means- but it is not obvious to me what this means.
Do they want a published paper/published review article? But then, it is likely to have co-authors so it is not my writing sample. If not, what do they mean by "paper"? A critique of a research paper is hardly a few pages, let alone ~20. For a scholarly paper I'll have my bachelor's thesis but it will be there towards the end of my bachelor's, much later than most admissions deadlines. What do such submissions expect?
When I mailed them, they replied the following which doesn't make it clear to me what is expected (or common):
The application requires a writing sample. For our program, there are no rules regarding the writing sample so it can be a piece your own choosing.
Note: Most of my work till now has been collaborative, and my background is a STEM subject.