This is one of those posts. You know, the ones I write so I can just post a link rather than say the same thing over and over again and again and again ... ad nauseam.
My opinion will probably change at some point, because I'm flexible like that, but for now I'm venturing into the grimdark/horror arena for a reason. Yes, yes, I know all about Warhammer 40K "In the grim darkness of the far future, there is only war ..." so if you comment about Warhammer 40K, I'm going to assume you just shot down to the comments to tell me about Warhammer 40K without reading the actual post.
I'm not trying to invalidate the Warhammer 40K definition. "In the grim darkness of the far future ..." was the beginning. Anyone who says that the grimdark was born of this statement isn't wrong; however, while Warhammer 40K might be the root of the grimdark phenomenon, the branches of that vine have extended to encompass a lot of things outside of Warhammer 40K, and so here we all are ...
What follows is my personal definition. If you need something that cites several articles, look anywhere but here, because I don't have time to chase citations right now. The quick and dirty way I differentiate grimdark from horror is simply this:
Horror--a story where the protagonist is helpless in the face of a supernatural threat. It is an ordinary person against a much more powerful supernatural adversary. The protagonist seeks to destroy the supernatural threat in order to save themselves or others, but only when they are forced into a confrontation. The horror elements in the story are culled from the protagonist's increasing helplessness in the face of overwhelming odds.
Grimdark--a story where the protagonist faces a supernatural threat, but s/he isn't helpless against their adversary. Rather than run from the supernatural threat, the grimdark protagonist actively seeks to subvert or control it. In grimdark, the characters exhibit amoral [read: darker] tendencies, which replace the element of helplessness as the primary focus of the dread/horror.
There are supernatural elements in both, but they are utilized in very different ways. Both can also be violent and graphic. What separates them is the protagonist and how that individual deals with the supernatural threat.
If you've got a different definition, drop it in the comments. I'm always open to consider other viewpoints, but for now, that's how I'm defining the two.