There are two incarnations of Sub-Zero, both of whom are siblings: older brother Bi-Han, and younger brother Kuai Liang. Both are blue garbed warriors who, at different times, have used the codename "Sub-Zero", and both are members of the Lin Kuei. They are descended from Cryomancers, an exiled Edenian race possessing the ability to generate and control ice. However, they were born in Earthrealm and only the younger Sub-Zero would discover his heritage (in the original timeline).
Kuai Liang bears a scar on his right eye. In the original timeline, he received it sometime prior to the events of Mortal Kombat 3. However, as seen in Deception, the scar eventually faded away, possibly as a result of the Dragon Medallion's power. In the second timeline, revealed in the Mortal Kombat X comic series, it was Kano who created the scar.
Bi-Han and Kuai Liang were born to a Cryomancer father and a Chinese-American human mother. Their father was a secret operative for the Lin Kuei in the United States, eventually taking both sons back with him to China, against their mother's wishes. The brothers would then be trained as Lin Kuei assassins. However, this is no longer canon. It has since been established that both brothers were kidnapped by the Lin Kuei when they were still children as was revealed in Sub-Zero's trailer for Mortal Kombat (2011).
Bi-Han appeared as Sub-Zero in the first Mortal Kombat tournament, while Kuai Liang went by the codename "Tundra". After Bi-Han was murdered by Scorpion, Kuai Liang swore to avenge him. He took his brother's former codename, Sub-Zero, as a means of honoring his brother. He entered the second Mortal Kombat with only one goal in mind: hunting down his brother's killer.
Kuai Liang would bear the name Sub-Zero in all future games, whereas Bi-Han would be resurrected as a wraith by [family=67023 and given the name Noob Saibot.
Although the two brothers differ significantly in many ways, they both share traits in common. Kuai Liang comes off as a menacing, stern, distant, and cold man who prefers to remain in the shadows, not unlike his elder brother. However, Kuai Liang is more serious, disciplined, humane, and honorable than Bi-Han ever was. In contrast to his older brother, who eventually succumbed to darkness, the younger Sub-Zero remained firmly on the side of justice. This vast disparity caused the two siblings to disown one another, stating "we share blood, we are not brothers".
Kuai Liang's strong moral principles have also brought him into conflict with his own clan. Horrified by the Lin Kuei's cyberization initiative, Kuai Liang openly rebelled and eventually left the clan altogether in horror and disgust, thereby breaking the sacred codes of honor. In response, his former clan marked him for death, programming Cyrax, Sektor, and his former friend Smoke to hunt down and terminate him. Kuai Liang subsequently joined Liu Kang, Raiden, and Earthrealm's other defenders in the struggle against Shao Kahn.
In both timelines, the younger Sub-Zero defeated and killed Sektor, becoming the new Lin Kuei Grandmaster in the process. Under his stewardship, the Lin Kuei would be reformed and rebuilt into a force for good.
Like most of the MK cast, Kuai Liang follows a character archetype. In his case, he is the enigmatic hero who shows up to aid the protagonists when needed.