The so-called narrative, argumentative, expository and practical writing itself includes two categories: literary works and applied documents. In fact, these terms are widely used in school work. The division is not very strict, for example, explanatory writing belongs to practical writing in a strict sense.
Prose is the genre of literary works. Prose in a broad sense includes argumentative prose, narrative prose and lyrical prose, but generally does not include expository prose and practical prose.
Therefore, it can be said that narrative, argumentative, expository and so on all intersect with prose.