There's no Sub-Zero (III). Deception's Sub-Zero is Sub-Zero (II), just as he has been since MK2.

I believe that there has been a single Sub-zero since MK2...and it is the earth-allied good-natured Sub-Zero. So the Sub-Zero in this game is the same man that has been in MK2 - MK:Deception. Since Sub-Zero has not died since MK1.
The only time Sub-Zero has been evil was MK1, so when Scorpion killed him out of revenge, he went to the netherrealm and became a demon (Noob Saibot, obviously)...does that answer you question? A little confusing maybe?

yes, thanks to both

I've done a lot of "research" on Sub-Zero's storylines, trying to find the straight canon.
There have been only two Sub-Zero's, the two brothers.
In MK1, it was the older brother, and the evil one. There are many stories in which he is killed by Liu Kang, most that he was killed by Scorpion. Sub-Zero original killed Scorpion in combat before MK1 (Scorp then thought it was Sub-Zero who killed his family) but then he came back as the spectre we've always seen, and killed Sub-Zero original-- according to the non-Liu Kang story as seen in the movie.
After the death of original evil Sub-Zero, his brother, with the same powers and costume, came about. He was in MK2. He however was good, not evil. He's been the same one ever since then.
Now, in Deception, we learn that Noob Saibot is the original Sub-Zero. Apparently in the same spectre form that Scorpion returned in.
Now let's wait for the next game and learn more about Noob's transformation from Sub-Zero.

Now that we know Noob Saibot is actually the older Sub-Zero in disguise, it gives some insight to his storyline in MK3.
In MK3, Noob was ordered to serve Kahn until Shinnok says otherwise, then stab him in the back.
Classic Sub-Zero's story in MK3 was that he was still going after Shang Tsung, his mission from MK1.
My guess is that maybe Noob Saibot helped to weaken Outworld by attacking Shang Tsung AS Sub-Zero but then hiding in his Noob Saibot form. He eventually did betray Outworld, after all, and I think maybe Noob Saibot transformed himself into Sub-Zero at certain times to throw Outworld off.
Stupid theory, but I think it makes sense.