New Make, New Model, New Mission

It seems there's a lot of confusion about the Terminator's model and make. Especially after Terminator 3 has been released, in which they used the term T-101 to refer to the Terminator's model.

The most detailed information about the Terminator's model is given in the director's cut of Terminator 2. There's a small scene in which Sarah and John have to switch the Terminator's CPU from "read-only mode" to "read/write mode." As they put the CPU back in the Terminator's head, we get to see its bootup display, and the make and modelnumber is revealed at the top left: CSM-101 T-800 Version 2.4. We can split this information into 3 parts: CSM-101 (Model) & T-800 (Make) & Version 2.4 (Version).

Model

CSM-101 stands for Cyberdyne Systems Model 101, as Kyle Reese explained in the first movie. This part basically means the appearance of the mould around the metal Endoskeleton (the skin), and in this case, 101 refers to mouldnumber 101, the Arnold Schwarzenegger appearance and looks. Model-101 looks like Arnold Schwarzenegger, while Model-100 and Model-102 would look like someone else, etc.

In Terminator 3, the Terminator says "That was a different T-101." This confuses a lot of people, but it's easy to explain. The Terminator refers to it as Terminator Model-101, only meaning a Terminator with mould 101 (Schwarzenegger). This is not the make(/chassis) of the Terminator, which are explained later. It's just a sort of abbreviation, instead of having to say "That was a different Cyberdyne Systems Model-101."

Additional information:

Make

T-800 stands for Terminator 800 Series Systems. This is the chassis hidden underneath the skin, basically the make of the hi-tech Endoskeleton Series. The T-800 Endoskeleton Series Systems is just one of the many chassis production lines (see additional information for other examples).

Additional information:

1) The official movie site has a flash intro in which the term 'T-850' is shown. This caused quite some confusion in the beginning of the T3 movie hype.
2) The novelization has a scene in which the Terminator explains it a bit more. Here's the scene as it happens in the movie, followed by the exact same scene as it happens in the official movie novelization (check below)

Movie:

Novelization (by David Hagberg):

The only thing that his part of the novelization clarifies is that this Terminator is an upgraded version of the old T-800 Series Systems, with at least an improved chassis. What the other improvements are is hard to tell. I myself believe there must be some other differences, like the power supply. The Terminators in T1 and T2 both have just 1 nuclear-energy cell, while the Terminator in T3 is powered by 2 hydrogen fuell cells that will explode like small nuclear explosions when they have become unstable by rupture.

A small fact I want to add is that according to the novelization of T1 and T2 (both written by Randall Frakes), there was also a difference between the duration of the power cells of the T1 Terminator and the T2 Terminator.

The T1 novel says: "Terminator could keep operating at full power for twenty-four hours a day for 1,095 days."

The T2 novel (and movie) says: "A hundred and twenty years on my existing power-cell, under normal conditions.

One could worry about which is the most canon; the movie or the novel. In this case we take the movie for granted as the most canon, and it's best to ignore the fact of the T1 novel because both units should been complete identical. They came from the exact same rack out of the exact same cold storage room. It's just an interesting small fact to point at.

Version

Version 2.4 stands for Version 2.4.
This one is the hardest to explain, since no canon information has been released for it. Most people (including myself) see this as the versionnumber of the Central Processing Unit (CPU, the Terminator's brain). The updates that have improved the CPU. This could explain why all the different Terminators in the movies had all different TermoVisions. Here's an example of how the numbering works:

So for small updates, they'll change the decimal number after the dot, while with big updates, they change the number before the dot into a new following number and set the decimal number after the dot back at 0.