Master con man, a person who knows how to manipulate a dreaming mark into revealing their deepest mental secrets. At heart, an extractor is a classic con man - he creates a false set of circumstances that manipulate the mark into revealing his secrets.
The designer of the dream. Think of an architect as a video game designer, except in this case, they create the "levels" within a dream, complete with all the aesthetic and tactile details. The architect can manipulate real-world architecture and physics in order to create paradoxes like an endless staircase, which makes the dream world function as a sort of maze. The dream is constructed as a maze so that the mark doesn't reach the edge of the maze, realizing that they are in an imaginary place. As the mark runs the maze, the extractor is led towards the mental secrets that they are protecting.
The person who the extractor is trying to con. The mark is brought into the mind of the dreamer, and since the mark is unaware that they are dreaming, they perceive the dreamer's world as reality, therefore filling it with details and secrets from their own subconscious. The extractor uses those details and various mental prompts to steer the mark through the dream maze toward the mental secrets the extractor wants to steal. As stated, the mark thinks he is still awake, perceives the dream world as real, and reinforces that notion by "projecting" his conscious view of the world onto the dream - this is why projection people populate the dream cities, etc. Because of the extractor's manipulations, the mark goes along with the faux reality of dream, ultimately reaching the point where they either realize it's a dream or open their mind and reveal their secrets.
The person whose mind actually houses the dream. It is the dreamer's mind that the mark is ultimately brought into in order to to be conned by the extractor. The dreamer allows the mark to fill their mind with the mark's subconscious, and unless the dreamer maintains the stability of the dream, the mark's subconscious will realize it's been invaded by foreign mind(s) and will try to locate and eliminate the dreamer to free itself. Identifying the dreamer can be tricky. Once a tri-level dream sequence starts, one good way to keep track of the dreamers is by noticing which person stays awake and doesn't follow the team down to the next level of dreaming - a dreamer can't enter a lower dream state. Otherwise, their level of the dream would end.
As in "forgery," is a master of imitating people's handwriting, mannerisms - and in the dream world, even their appearance.
Dreams feel real to us when we're dreaming, and part of the reason for that is our mind's ability to construct a faux real-world setting for us to interact within dreams. Often, that dream is something like a city or any populated area which has other people walking around it. These seemingly “random” people that populate the dream world are known as "projections." As is explained in the film, projections are not part of the mark's mind - they are manifestations of the mark's vision of reality. If a mark has been trained to defend themselves against extractors, part of their subconscious will always be on guard against mind-crime.
