In the warhammer world, wights are essentially the same thing as mummies.
At the dawn of ancient Nehekhara, Settra commanded the priests and sorcerers of the land to research the means of immortality, that he could reign forever. These magi and magicians eventually became the mortuary cult. They did not find the secret of eternal life during Settra's time, but they did find a way to tear the souls of the recently dead from the warp and bind them to their dead bodies. On Settra's deathbed they promised him that this would allow them to restore him to life once the true secret was found, and he would indeed reign forever just as he commanded. They prepared and preserved his body as well as they could that it would not decompose before they could find a way to revive him, but the secret of that revival remained ever beyond their grasp, and in time their descendants were more concerned with their own contemporary political power than with reviving the ruler that their predecessors had made such extravagant promises to.
The methods they developed, careful mummification to preserve the body and rituals to bind the soul to it, became the common practice among kings, nobility, and great warriors in Nehekhara, and in later ages bastardized versions of this practice - which lacked the careful and expensive process of mummification but preserved the rituals that bound the soul, performed as funerary rites often without any knowledge of their arcane implications - spread to other cultures and lands, and persisted in the funerary rights even of the early Empire, and may yet persist in some of its more remote corners.
These are mummies and wights, corporeal undead that were once rulers, warlords, tribal leaders, and great warriors, and that maintain all, or at least a larger portion of, the original soul, along with a matching portion of their will and memory. They still need a powerful force of dark or death magic to wake their minds and animate their bones, which generally takes the form of a necromancer or liche priest casting spells to raise them from their tombs, but where and when the wind of death flows strongly enough wights may indeed rise on their own.
Once risen, they are capable of directing themselves, and even other undead, though a powerful enough necromantic will can bind them in subservience in turn. This is easier to do with wights that had their souls bound by inferior bastardized rituals of later cultures, rather than with the mummies of ancient nehekhara, whose souls, wills, and memories of life are generally more intact (though still in most cases they have been driven thoroughly insane by the passage of time and the sheer horror of their existence).