Ok this is a bit out of date now, we've seen the T-1 in the third Terminator movie but at this stage they are never referred to as Terminators. The T-1 was still created by humans but I wonder if the T-600 (machine skeletons covered in rubber skin mentioned in the original movie) is the first one designed by Skynet specifically for the war against humans. That would make the T-600 the first actual Terminator and also mean that Terminators was a name the machines gave themselves?
Of course then you need another explaination for what the T stands for in the T-1's
.