Just in case you’re serious:
There are now four Terminator movies–well, three full-length movies and a stage-show/movie at Universal (quite good, by the way, I recommend it if you’re a Terminator fan and are at Universal Studios.) In the first one, made in 1984, the Terminator, played by Arnold Schwarzenegger, was sent back in time before Sarah Connor, played by Linda Hamilton, was pregnant with her son and eventual leader of the human resistance, John Connor. Skynet is the AI that destroys most of the world with nukes on, I believe (and if I remember the code correctly for the third ending on the T2 DVD), August 29, 1997, and sends the Terminator back to take out Sarah Connor. Unlike the next two movies, Sarah Connor’s protector was a human member of the resistance, Kyle Reese (played by Michael Biehn), sent by in time by John Connor to protect his mother before he was born. The Terminator (a T-100 or T-101 model, I believe, though other sources say T-800, so I don’t know, the whole thing is kind of screwy) was a killing machine, pure and simple, taking out anyone who was in the way of the goal. Sarah and Kyle wind up taking out the Terminator by, if I remember correctly, crushing it under a hydraulic press, and the two of them wind up having sex (before the crushing of the Terminator), making Reese the father of John Connor.
The Terminator didn’t really need a sequel, but making one wouldn’t really have a feeling of screwing everything up, so they, of course, wound up making another one in 1991.
Now onto the next movie. In the next one, Terminator 2: Judgement Day, the T-1000, played by Robert Patrick, is sent back in time to kill John Connor, played by Edward Furlong, at the age of–well, the continuity is kinda screwed up, but either 10 or 13. Future John sends the Terminator (different one, same model, and once again played by Schwarzenegger) back in time to protect himself as a boy. Of course, they have to bust Sarah out of a mental institution, which leads to several misunderstandings, chase sequences, fights between the Terminator and T-1000, the destruction of the original arm and chip leftover from the first Terminator that is housed at Cyberdine, the company that eventually makes Skynet, as well as the destruction of both the T-1000 and the Terminator by being dipped in liquid iron.
Now, if the first movie didn’t need a sequel, the second one really didn’t. And this is where things stood until the mid-to-late 90s, when they decided to design that show.
Now, it’s a pretty good show. Once again, surprise surprise, Skynet is trying to kill Connor. The Terminator comes back, saves John, (both Schwarzenegger and Furlong reprising their roles) and they (and the audience, thanks to some pretty good stage and 3D effects) go into the future to confront Skynet. They wind up destroying at least part of Skynet and the T-1,000,000 (seeing a pattern here, yet?) and everything goes back to more or less normal.
As I said, a pretty fun thing to go to. But anyway, I’m just mentioning this here for completenesses sake.
So, now we come to Terminator 3: Rise of the Machines. Once again, Skynet has sent a new model back to kill Connor (now played by Nick Stahl); this time the TX, played by Kristanna Loken. She’s actually pretty cool, combining some of the design of the T-100 (or whatever) with the T-1000, plus the ability to actually mimic more than just blades and people by using nanotech. The Terminator is once again (and once again, same model, different robot) sent back in time to protect John and his future wife, Kate Brewster (played by Claire Danes), this time by Brewster. That’s all I’ll give here, seeing as how some people probably haven’t seen the movie or read the spoilers.
So basically, while Schwarzenegger was the Terminator all the time, the first time he was playing a Terminator that was out to help destroy humanity, and then for the rest to help save humanity.
Oh, while they’re all technically Terminators, generally only the one Schwarzenegger plays is called THE Terminator, all the rest are called T-1000 or the T-X or whatever.