We're just using a familiar metaphor (movies/theater) for talking about all the same elements that are fundamental within RPGs. The primer strives to introduce the basic metaphor and the terminology mappings in the early going, but it apparently fails to do a good job of it.
So let me try again here...
In a movie, all the actors play everything out on the stage (or set). There are the major characters (protagonists and antagonists). There is the supporting cast (helpers for the heroes, lieutenants for the villains, and just color). And then there are the extras (mooks for the villains and background folks for the heroes).
A movie is constructed of scenes. Each scene starts with a script. Within the script, there are stage directions of varying types. And once the director and cast get their hands on the script, there are tweaks and adjustments, with each principle contributor making their own notes.
When the director yells "Action", everything plays out on the stage. Sometimes a scene goes exactly as the script says. Other times, it goes wildly different when the stars improvise. Just think of the "sword fight" from Raiders of the Lost Ark or Robin Williams as the Genie in Aladdin.
Once the director yells "Cut", the scene is complete. In the movies, scenes can have numerous takes and then get edited into the final product. In stage theater, each night is a unique performance with no do-overs. RPGs are much like improvisational theater in this respect.
So let's take a look at RPGs now. The GM prepares the overall script for the entire adventure, mapping out each individual planned scene (aka encounter). The PCs are the protagonists, the villains are the antagonists, and there is a huge supporting cast of NPCs, ranging from pivotal characters to entertaining color to disposable extras (e.g. tavern patrons, beggars on the street, etc.). Hopefully, that sounds pretty similar to what I outlined above for a movie.
When a scene begins, the GM sets the stage. He determines where everyone is placed, what their motivations are, and how they'll react in varying situations. Then the PCs step in and the action begins. The PCs then write their own version of the story within the framework of the overall adventure the GM created. The GM can shape it, but the choices the PCs make ultimately dictate how everything unfolds.
So the GM is essentially the primary writer, director, and producer of a movie (aka the adventure). And it all plays out on a stage that frequently doubles as the dining room table.
Now that the abstraction of the metaphor is established, let's look at the mapping to CT in a more concrete manner...
Within CT, each campaign is an independent production, with its own script and cast. The PCs are the protagonists. All of the NPCs are cast members of varying importance. Each scene has a script that identifies who's in it (along with detailed notes in the near future). Cast members (NPCs) that have recurring roles are kept in a pool that can be drawn from at any time. A cast member that only appears in a single scene will exist solely within the script for that scene.
Everything in CT takes place on the stage. The stage is a summary view that is visible to the GM and players alike. It keeps everyone aware of who's involved in the current scene, and what state everyone is in. The GM gets to see all the details, while the players can see details of the PCs but only the basics of other cast members (the NPCs). In story mode (i.e. outside of combat), the stage presents a convenient overview for everyone. When it's time to go on initiative, tactical mode tracks all the niggly bits so everyone knows whose turn it is, who's up next, who's holding their action, etc.
By default, all the PCs are automatically added to the stage when the GM starts a game session. The GM can then enact the prepared script for a scene with a few clicks. All the cast members in that scene are placed on the stage, and the scene can then be played out efficiently. When a scene is completed, the GM resolves the scene, which creates a permanent record of the scene. Combined with completed sessions, both the GM and players will have a full history of the campaign available for reference. [Note: the permanent record mechanism is not yet in place, but it's definitely planned.]
That's just the most basic overview of what CT provides. We have a very long list of really cool features (IMO) that we'll be adding to make CT an incredibly flexible and powerful tool. Our goal is to create a tool that eases game preparation for GMs, streamlines play for everyone, and provides an historical record to facilitate answering questions about past sessions.
I hope this was helpful to some of you out there. Please tell me where to focus and I'll do my best to explain further.