Ok, Here we go...
MK1: Sub-zero the elder. He is the older brother of the MK2-MKD Sub-Zero. He is also the star of MK: Mythologies. He killed Scorpion, who as a wraith came back for revenge in MK1 and eventually kills sub-zero the elder. Sub-Zero the elder had a seed of evil in him which was revealed by Raiden in MK: Myths. He dies and is sent to the netherrealm.
MK2: Sub-Zero is back. Scorpion thinks it is the original he had killed in the previous tourniment. He stalks him, but sees him spare the life of an opponent. Knowing the orriginal would never spare an opponent, Scorpion vows to attone for his murder by becoming Sub-Zero the younger's guardian. Over the course of the tourny, it is revealed that the Subby in this tourniment is the younger one.
MK2 part 2: Noob Saibot makes his first appearence. He is a servant of Kahn. Not much is said about him, being a hidden character, but he appears non-the-less.
MK3: Sub-Zero the younger is once again in this game. His scar is said to be from his escape from his clan during the time they started making robots (This is later contradicted by Shaolin Monks, where you give him his scar in a fight). He has no Lin Kieu(SP?) garb, showing him not to be the original.
MK3: Noob-Saibot: Once again he is an assasin. Many theories pop up about him. He is once again Shao Kahn's assasin.
Umk3: Classic Sub-Zero: This was put basically as a filler, and to have Subby get his Cool clothes back.
Mk4: Sub-Zero: He is still the younger. He learns of Shinnoks invasion and accompanie the earthrealm warriors to defend edenia. He wears his brother's old clothes in his honor(the Lin Kuei being disbanded) after finding out his brother's ordeals with Shinnok over the amulet. This is also where we find out who caused Scorps vendetta against Subby.
MK Gold: Noob Saibot: He is reviled to have been working for Shinnok and Quan Chi the whole time. He is there assasin/informant working for them since his death at the hands of Scorpion. It is either here, in mk3 or in mkd that we actually get confirmance that he is the original.
MK Deadly Alliance: Sub-Zero: He appears much older than previously thought. His scar is now blue instead of pink, the most common theory being that his Dragon Medallion is giving him advanced powers, also changing. He reforms the Lin Kuei, and gets an apprentice, Frost. He travels to attack the DA, but is side-tracked when Frost steals the Dragon Medallion and dies.
MK DA: Noob: Not in it, presumably finding Smoke in Kahn's fortress around now.
MK Deception: Sub-Zero: He finds his ancestial armor at Frost's burial site, which also show's that he, Frost, and his brother have ancestors from outworld who also could control the cold. He doesn't do much, the most controversial thing is his scar's dissapearence. The most accepted theory is the Ancestial armor has healed him, and also advanced his powers.
MK D: Noob(Smoke): Noob is now beyond a doubt shown to be the original sub-zero. He is Goro's *slayer*(disprove(?) by the GC version). He reactivates Smoke, his *old friend*, and in his ending he kills his brother Sub-Zero, once again proving beyond a doubt that his is Sub-Zero the Elder.
So, Noob= Original Sub, Sub=Sub we used in MK D.
The Scar Theories: If you skipped down to the end, is the Dragon Medallion has critacally changed Sub-Zero down to his skin, which cause the scar's color to change, and eventually, with the addition of the armor, dissapears.