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.