I'm having trouble distinguishing between the three. What are the major differences between these types?
Let's break it down.
In official canon, there are no Light Sith. This is because the very existence of the Sith is an affront to the Force, due to the way they use it.
In Legends (EU) canon, however (specifically in the Star Wars: Old Republic MMO), Light Sith are adherents to the Sith order who utilize the Light Side of the Force (and perform acts accordingly). Due to their different approach to things, they are labeled renegades and hunted down by the other Sith. The exception here is the player character in The Old Republic, who can manage to play off their actions as pure pragmatism.
Grey Jedi is a Legends canon term referring to trained Force sensitives who could potentially use both the Light and Dark Sides of the Force, but more importantly worked toward personal ethics rather than those established by the Sith or the Jedi order. Originally, the term was specifically meant for Jedi who left the order due to ideological differences. In the years that followed, this term started also being used for those trained Force sensitives from orders unrelated to the Jedi.
Dark Jedi use the Dark Side of the Force, but are not Sith Lords. In present canon, that includes trained Force sensitives from outside the Jedi order, such as Asajj Ventress.
In the Legends canon, Dark Jedi reject the Light Side of the Force entirely; they hold an axiomatic position which rejects the Light in favor of the Dark. The first Dark Jedi started the order known as the Dark Lords of the Sith, which was related ideologically (and, in some cases, genetically) to the Sith Empire.
Its quite elementary. Think of it this way - the Jedi Order did NOT always exist. In SW Canon, the Dark Siders (eventually the Sith) branched off from the Order during the early years of the Jedi. The Force however, like a Universal Law, has and will always be in existence and is the original source (or mojo sauce, if you prefer ;-) as described by Master Yoda. It is everywhere and in all things, which means it encompasses BOTH good & bad, light & dark sides.
George Lucas basically copy-pasted some ancient Eastern Mystical traditions wherein all duality (or dualistic conceptions) is an illusion.
The Jedi is merely a structured organization, for better or worse. Its identity as a coherent hierarchy comes & goes or be called by different names (by different species) in the long arc of SW Galactic history. By convention, any being "trained" (no definition of for how long) by this group implies he/she becomes a "Jedi".
Luke becomes a "Jedi" because he got what little training from Master Yoda even though he didn't actually "finish" his training course work. Lol. Same with many of the Sith "apprenticeships" whereby many of their "Rule of Two" often ends prematurely.
Furthermore in official SW movies, there were non-Jedi and non-Sith trained beings who had naturally-acquired "Force" powers. E.g.) the "Broom Boy". These could probably be called "Grey Force Users" but non-Jedi, and how they utilize their gifts will determine whether they lean more on the "Light" or "Dark" spectrum.
Therefore, there is definitely "Grey Jedi" and every shade in-between both ends, just as there is every shade of lightsaber colors.
Strictly speaking and in actuality, the definitions of "color" itself is also merely by convention, since all colors blends into each other seamlessly in the EM spectrum. There is really NO non-arbitrary marker to say Blue starts at this exact wavelength/frequency or Green ends at some other point on.