It all hinges on implementation, but as Kilolo states, the room for differing interpretations is just that vast.
Personally, it comes down to believability: If the character's motivations are shallow and they are portrayed in a... plastic manner, that is, their actions, while psychotic/deranged/amoral, are so in a contrived manner epsecially geared toward evoking a reaction, any reaction, from the reader, that's edge.
I'd say dark is where not only the character's actions are believable, but also their motivation, whatever that might be. The author does not seek to purposely elicit shock or revulsion, yet the dark character ends up doing so more than the edgy one, for the darkness runs to the root of the psyche instead of being a shallow display of repulsiveness.
I'd compare it to being assaulted by a guy in a fur suit(edgy) vs. being chased by an alpha lion(dark).
In the former scenario I'd try for a knee to the crotch, the latter I'ma run for a tree.
Again, Kilolo is right, just my personal ramblings.