Story and narrative are not the same thing either. Narrative is the order of events into a plot, to tell a story.
The definition of narrative is thus; 1. a spoken or written account of connected events; a story; 2. the practice or art of telling stories; 3. a representation of a particular situation or process in such a way as to reflect or conform to an overarching set of aims or values.
Story is defined as such; 1. an account of incidents or events; 2. a statement regarding the facts pertinent to a situation in question 3. a fictional narrative shorter than a novel; specifically, short story; 4. the intrigue or plot of a narrative or dramatic work 5. a widely circulated rumor
All stories are narratives but not all narratives are stories.
As a subgenre, Grimdark is described as having the qualities; a subgenre or a way to describe the tone, style or setting of speculative fiction (especially fantasy) that is, depending on the definition used, markedly dystopian or amoral, or particularly violent or realistic. The word was inspired by the tagline of the tabletop strategy game Warhammer 40,000: "In the grim darkness of the far future, there is only war."
To which the cited authorial examples are; "where nobody is honourable and Might is Right", and as "the standard way of referring to fantasies that turn their backs on the more uplifting, Pre-Raphaelite visions of idealized medievaliana, and instead stress how nasty, brutish, short and, er, dark life back then 'really' was."
"Shorthand for a subgenre of fantasy fiction that claims to trade on the psychology of those sword-toting heroes, and the dark realism behind all those kingdom politics"
"A retreat into the valorisation of darkness for darkness's sake, into a kind of nihilism that portrays right action ... as either impossible or futile". This, according to her (the author), has the effect of absolving the protagonists as well as the reader from moral responsibility.
Modern dictionaries define Grimdark as having it's origins in the combination of Grim + Dark. Grim defined as; 1. forbidding or uninviting; 2. (of humor) lacking genuine levity; mirthless; black; 3. depressing or worrying to consider.
Dark is defined as such; 1. with little or no light; 2. (of a color or object) not reflecting much light; approaching black in shade 3. (of a period of time or situation) characterized by tragedy, unhappiness, or unpleasantness (synonyms tragic, disastrous, catastrophic, cataclysmic, awful, dire, terrible, woeful)
In his blog 'Grimdark' author Joe Abercrombie states; "Grimdark Fantasy, gritty fantasy, is a reaction to the clean, romantic-heroic fantasy that has come before, it is a counterbalancing to a more straightforward style of fantasy."
We have no indication at all that the style of Grimdark is as used in narratives is values or seeks to evoke hope. All use of language around Grimdark is exactly the opposite in practice and diction.
I added emphasis to forms taken from the Wiki, Merriam-Webster, Joe Ambercrombie's blog, the literature subbereddit, Grimdark Reader, Google Books and Renai LeMay literature blog.