Although these two terms are often used synonymously, there are actually many significant differences between Sith and Dark Jedi (also known as Fallen Jedi, for reasons that are mainly self-explanatory). The most basic distinction is in the origin of each type: the Sith themselves were originally a species, originating on Korriban, long since extinct, but naturally strong in Force Sensitivity, although they exploited this through the use of magical incantations and formulas, much like the Dathomir Witches, rather than through simply using the Force in the way that the Jedi have always been known to do. Millenia ago, several Jedi that had been exiled from the Jedi Order for advocating a path that required that the individual used emotion, enslaved the Sith as their Gods and eventually became known as the Lords of the Sith.
Over time, these Dark Lords inevitably adopted many of the cultural aspects of the Sith, primarily including their language and magical incantations, learning things about the Force as a result that the Jedi had never taught, thus creating a schism between the abilities of the Sith and those of the Jedi. In honouring the legacy of Darth Andeddu, all subsequent Sith Lords took on the title of 'Darth', immediately followed by a pseudonym which remained their secret name among the Sith, not to be revealed to outsiders. More often than not, these adopted names became the Sith's permanent names, their original names discarded and forgotten.
Dark Jedi, on the other hand, are not members of the Sith Order, although the original Dark Lords of the Sith were indeed Dark Jedi, but instead these are simply members of the Jedi Order that have 'fallen' or turned away from the Jedi teachings to follow the 'Dark Side of the Force', whereby they act out of emotion, rather than from mindful serenity. In doing so, they also connect to the Force in a far different way to those advocated by Jedi teachings - rather than channeling the energy of the Force that flows through them, instead they use their emotional energy to use the Force as a direct tool, thus meaning that Dark Jedi techniques are far more overt and aggressive in nature than the more passive Jedi skills.
This in itself provides one of the more major differences between Sith and Dark Jedi - the types of abilities which the two possess. Dark Jedi traditionally utilise corrupted Jedi teachings and abilities, so more often than not they possess similar skills like Force Kinesis, Affect Mind etc, simply drawing on a different approach for using those skills. Additionally, the Dark Jedi also lack the same restraint and ethical tendencies of the Jedi, so can turn their powers into less moral uses - a major example being the use of Force Kinesis to choke an adversary, or using a dominating Mind Trick to force another to serve their whims. The Sith, on the other hand, use mainly abilities that originate with the Sith race that they enslaved, and hence have a far wider range of abilities than Dark Jedi, the most prominant example being that of Force Lightning, which stems from a Sith incantation that eventually had the verbal component removed.
While it is certainly true to say that the Sith can use the powers of both Jedi and Dark Jedi, albeit in a form not restricted by the Jedi's ethical tendencies, and feeding off the Dark Side of the Force like Dark Jedi do, inevitably the reverse is not true - one cannot use Sith abilities without being trained in the Sith arts (thus becoming a Sith), consequently meaning that Dark Jedi are far more restricted in their powers than the Sith.
Additionally, there is a major difference in the philosophies of the two. The Sith have a long and ancient tradition which all Sith adhere to, whereas Dark Jedi are merely those that have turned away from Jedi practices, and thus, they have no set philosophy to adhere to - the only major similarity between the two in this regard is that both ascribe to using the Dark Side of the Force. The Sith have set traditions regarding several points: firstly, the use of emotion instead of serenity (a counter-Jedi philosophy), the idea that only through using emotions could one truly understand the Force, since emotions were completely natural to all sentient life, and to control them and suppress one's own instincts for power and progression was heretical - hence why the Jedi and Sith have always been opposed to one-another.
Secondly there is the belief in the doctrine that life only becomes truly strong in conflict - following on from the Darwinian idea that evolution occurs from adaptation to environmental stimuli. Hence, in periods of war, those that are strong become much stronger, surviving and coming out of the war far more powerful than they had been before, whereas those that were weak to begin with perish. Inevitably, this improves the overall power of the species - and the Sith believe this is the key to understanding the Force, since this is a natural process, that the strong succeed where the weak perish. Consequently, the Sith prefer to be the ones responsible for the aggression, using it to increase their personal power, and to cull the weak that they might benefit from the strong. Unfortunately, this tended to be the downfall of the Sith, since their beliefs in their own strength were obstinate to the point whereby they often underestimated strength in forms other than the ones which they were used to - hence the inevitably withdrawal from the Sith existing en masse to the creation of the Rule of Two.
As a sidenote, this was an ancient doctrine that began following the Battle of Ruusan where both the armies of the Jedi and the Sith were destroyed as a result of a Thought Bomb, leaving only Darth Bane as a survivor. He came to realise that the failure of the Sith was in giving their adversaries a face to match the name - the Sith had up until that point existed in large numbers, and thus they had become an enemy towards whom it was easy to direct the arsenal of their inevitable defeat. Consequently, it is now Sith philosophy that the Sith exist only via the Rule of Two - that at any one time, only two Sith may exist: a Master and an Apprentice, one teaching the other. When it is time for the apprentice to train someone themselves, and once their own training is completed, it is customary for the Apprentice to murder their Master - if they fail, it is assumed by the Sith that the apprentice was not strong enough, and thus the Master seeks out a new student to train.
Dark Jedi are different in this regard, since they do not strictly speaking have to follow a path to dominate or control - instead, they can simply learn to use their emotions to channel Dark Side energy. What they then do with that is entirely at their discretion, whereas for a Sith, this is not so. Indeed, it is quite possible for a Dark Jedi to exist that uses their powers for good, although sadly this has never actually occurred, since very few Dark Jedi are strong enough to resist the inevitable corruption they face when utilising the Dark Side of the Force.
