In The Terminator, the cyborg assassin is the T-800.
More precisely, Arnold Schwarzenegger's machine is identified in the early films as a Cyberdyne Systems Model 101, part of the Series 800 line. It is a robotic endoskeleton covered with living human tissue, allowing it to infiltrate human communities while possessing immense strength and durability. In the 1984 film, Skynet sends it from 2029 to Los Angeles to kill Sarah Connor before she can give birth to John Connor, the future leader of the human Resistance.
The T-800 is often simply called “the Terminator,” but that label can also refer generically to other assassination machines. The T-1000, for example, is the liquid-metal antagonist of Terminator 2, while the T-X appears in Terminator 3. Those are different models, not alternate names for the original assassin.
A notable twist in the sequel is that a T-800 is reprogrammed and sent back to protect young John Connor. The same basic model therefore changes from the first film's relentless villain into a reluctant protector.