Well - the Chef's Choice knife sharpener is a series of generally 2-3 grinding stones (depends on model) set at a fixed angle on a shaft rotated by an electric motor. The swirls can come from the amount of pressure you apply to the knife, the speed you draw it through the sharpener, or the angle you hold the blade - of a combination of these.
"It ain't what you don't know that gets you in trouble. It's what you know for sure that just ain't so." - Mark Twain