The term “Dark Jedi” came from the early days of the EU to describe a evil
Force user. The word came before the Sith were a thing.
The Sith were "a thing" in the original movies. It's a term that dates back to the early drafts of the ANH script and showed up in all kinds of merchandise describing Vader as "The Dark Lord of the Sith" WAY before the EU days.
As for "Dark Jedi" as a term; well 1) the fact that the EU used it doesn't make it a good term, just one that exists, 2) IIRC it first showed up in the old WEG books, which as a role playing game is want to provide the players with options and rulesets they can use. So yes, if they want to play someone that's like a Jedi but is dark side then they copy the baseline "Jedi" rules across with a few tweaks and called them "dark Jedi" for ease of reference.
It's kinda like how in video games like Jedi Outcast & Force Unleashed there's such a things as "force powers" that have to be "activated" and expend points to use, and one set of powers is for the light and another for the dark...and yet none of that is even remotely how the force works; it's just how it's adapted and translated to worth within the gaming mechanics.
You can't be a "Dark Jedi" any more than you can be a "Grey Jedi". You're either a Jedi, or not. It's a religious order of warrior monks, it's not a weekend book club. Same goes for the Sith, only they have a MUCH more exclusive membership policy.
If a character WAS a Jedi and they turn to the dark side and consequently leave or are expelled then they're not necessarily anything in particular. Unless they join or found some other group (like say the Sith or the Ordu Aspectu) they're just themselves. Same goes for people like Ahsoka or Eeth Koth who were no longer Jedi because basically "fuck that noise". They're nothing in particular, just following their own path like most everyone else.
Now it'd be nice if there were a term in Star Wars like "Ronin" which indicates "a lone wanderer trained in the Jedi arts", but as of yet they're isn't. It's a shame, but here we are.