To the people of the Galactic Republic, where the Jedi Order is a stakeholder in public life and the primary representative of Force-calling groups, all of these groups appear to be Jedi. But in reality, they are not the basis from which all have developed. On the contrary. They are only one of the results, and only the most present in the areas controlled by the Republic. Other organizations of Force users exist, independent and unrelated to them (Baran Do, Aing-Tii monks, Tund wizards ...). However, there are many individuals and groups who are descended from the Jedi but who have separated themselves from the authority of the Jedi Council. They are then called Gray Jedi.
It is very difficult to define a gray Jedi, because then you have to define what a Jedi is. There are two opposing schools of thought. Is it the training, provided by masters appointed by the Jedi Council, which ensures to fit into the history of the Order? Or is it a common spirit, a will to act in a certain direction? For some groups like Corellia's Green Jedi, it's pretty straightforward. The only difference is in their allegiance, which covers a different area and boundaries. But for others, the definition of a Gray Jedi can be turned upside down. If it's training, then a Gray Jedi is someone who took part of their lessons before leaving or being kicked out of the Order. And he will keep that status no matter what, even if he joins a competing or even opposing organization. If this is the common spirit, then any Force user who calls on the Light side without obeying the Jedi Council can carry this title of Gray Jedi. In any case, there is an often-repeated mistake that can be safely contradicted: a Gray Jedi is in no way a Jedi who draws his powers from both sides of the Force.
Whatever definition is given to the Gray Jedi, those who indulge in the Dark Side receive another title: that of the Black Jedi. Except that the basic definition implies a change to this second definition. If training is at the heart of all this, then a Black Jedi is a member (and not necessarily an elder, a Gray) of the Jedi Order who has gone wrong. There are several who work within it, in breach of the Council's orders and thus acting illegally. If it is the common spirit that dominates, then the Black Jedi are to be distinguished from the Gray Jedi. The two groups find a common non-allegiance, but their exploration of the Force takes place in opposite directions. Black Jedi are feared in the galaxy as they regularly seek to seize power in their spheres of influence. Which led to many wars, in which the Republic and the Jedi Order had to intervene.
The Sith are to be considered as special within the Dark Jedi. The latter are generally poorly organized, gathered in groups too small to have a certain orthodoxy or even solitary. The Sith as we know them were born from the meeting of two groups of followers of the Dark side: renegade former Jedi and totally different wizards with their own cultures. The commonalities are as numerous as the differences, but there is also a political element to take into account. During the Great Hyperspace War, the Sith Order split into several parts. The Empire of Vitiate and the Dark Council is one of them, surely the most important. To strengthen their legitimacy, its representatives do not hesitate to denigrate their rivals from other branches. And for that put them back as much as possible in the simple category of Dark Jedi.