Originally Posted by Taco John
The Wights are the Zombies. The White Walkers are a separate race of intelligent creatures who animate the wights as their army. The white walkers are not zombies - they create them.
That's basically how I understand it, too, but it's kind of intentionally mushy.
Here's what I understand:
Roughly 12,000 years ago, an ethnic group of humans (now referred to as "The First Men") invaded Westeros across a land bridge from the east. They found that the land was already occupied by a race of being called the "Children of the Forest." These beings were smaller, less numerous and less technologically advanced than the invading humans, but they had access to "nature magic."
After generations of warfare, the First Men gradually pushed back the Children of the Forest and establish dozens, if not hundreds, of small kingdoms.
About 10,000 years ago, a truce was reached, whereby the Children were given dominion over the major forests, while the Men occupied the open lands. Except for a group who adopted "The Drowned God" (in the Iron Islands), the First Men adopt the worship of the Old Gods of the Forest.
About 8,000 years ago, the "Long Night" descended and presumably lasted for nearly an entire generation. A long and savage winter moved south, and with it came "The Others." The "Others" were able to kill people and then raise them up as undead servants (zombies or "wights.") They were eventually driven back by the First Men, led by a legendary hero called "Azor Ahai."
Subsequently, with the aid of magic, giants, and (possibly) the remaining Children of the Forest, they constructed the great ice wall to keep the "Others" out. The Night Watch was formed to guard it.
At this time, there were still some people living north of the wall (calling themselves "The Free Folk" but known to southerners as the "Wildlings.")
Not long after, one of the Commanders of the Night Watch, supposedly seduced by one of the undead, declared himself the Night King, and used the Watch as his personal army and committed all kinds of atrocities. He was defeated by an alliance between the Starks of Winterfell and Joramun, a Wildling leader, also known as "The King Beyond the Wall." Afterwards, the Night Watch was restored.
Thousands of years go by and all of this falls into myth and legend. Over time, the Wall becomes mostly a barrier to prevent Wildlings from raiding the southern side.
In the legends of southern Westeros, the undead are referred to as "The Others." Close to the Wall and North of the Wall, those same beings are often referred to as "The White Walkers." One gets the idea that the legends don't necessarily distinguish between the intelligent masters (who may or may not be undead spirits) and the more or less mindless wights (who they have apparently raised from the dead to serve as minions.) Likewise, various characters in the book don't necessarily distinguish between them at the outset since they don't really know what they are dealing with.
Additional things that still aren't clear. It's not clear what kind of ritual is needed or what it's range might be in order to raise people as zombies. Or whether it's more or less automatic. (It certainly isn't automatic south of the Wall - at least not at this point.) It's also unclear whether the intelligent "Others" have their own bodies or are somehow possessing the bodies of the living. The whole thing is still uncatalogued (and probably scarier as a result of that).