The terminator is the line that divides the sunlit and night-darkened parts of a planet. That was the original (1770) meaning and it's still used today.
That's because the Latin terminus meant boundary or limit, from which we get bus terminals, terms and conditions, fixed term parliaments and indeed many terms for things (because a term has a limited meaning).
As Tennyson put it:
Be near me when I fade away,
To point the term of human strife,
And on the low dark verge of life,
The twilight of eternal day.
Anyway, from that you get the idea of terminating somebody's employment. Legally speaking, you can do this two ways: you can terminate without prejudice, meaning that you are open to the idea of re-employing them, or you can terminate with prejudice meaning that you will never hire them again. The latter is for employees who have done something awfully naughty and broken your trust.
The CIA employs agents. If you break the CIA's trust and reveal secrets to the other side, your employment will be terminated. Indeed, it will be terminated with prejudice. Indeed, the CIA may make sure that nobody ever employs you again by the simple expedient of murdering you. This they jokingly refer to as termination with extreme prejudice.
The CIA being awfully secret, it's hard to say exactly when the phrase was invented. It's first recorded of a double agent in 1969. The important thing for us, dear reader, is that it is this usage that took the word terminate away from astronomy, contract law and bus depots and made the word big and tough and scary.
And thus and therefore the T800.
As an interesting point of technique: James Cameron just wanted to have a scene where a lorry explodes and then a robot walks out of the burning wreckage. The rest of the plot was invented to lead up to that one image. So the film was written from the end backwards. Compare Mickey Spillane's system explained here.
The Inky Fool's plans for world domination gather pace