If the US military retrived some pieces from the damaged terminator of the first movie and Cyberdyne systems took the rest then this would explain it. Cyberdyne Systems only seemed to have the arm and cpu from the original terminator endoskeleton. The rest could have been retrived by the military with clever Cyberdyne Systems employees somehow sneaking away with the Endoarm and chip. If an advanced robot with military implications was found in the real world it is certain the military would try its best to retreive any and all aspects of this technology.

In the film's timeline the military would develop terminator style technology while studying terminator pieces we did not see saved from the press in the first movie. They then would have a different numbering system such as T-101 instead of series 800 model 101 or T-800 model 101. Most likely though the writers of Terminator three were just being sloppy and that explains the different model numbering systems for the terminators.

In T3 Arnold is a slightly advanced terminator model or a 850 series model 101. Instead of calling him a T-850 they refer to him as a T-101. This can only be explained via the above reasoning of Cyberdyne Systems identification system no longer being used in future machines after it was destroyed and others had to carry on their research.