The diminutive spinning wheel shown in these photos would be called a castle wheel, so named for the number of 'spires' that rise upward. Castle wheels could be much larger than this though; that name referred more to the structure than to the size. The aspect of the size is what gives this spinning wheel the more common name of bride's wheel.
In the early 1800s, which is the probable date of this bride's wheel, and earlier, when a man and woman married, the woman left her family and moved to a new home, which was the choosing of the man.
Oftentimes, the young couple did not have a tract of land in the immediate vicinity of their families, and needed to travel a distance to start their home. The family might have only a single wagon on which to haul all of their possessions. The bride's wheel was created as a small, easily carried spinning wheel.
Because of its small size, the bride's wheel is often mistaken for a child's toy. But it is fully functional.
In the images, notice the small white balls on the ends of various turned parts of this wheel. The white balls are actual ivory. Also notice, in the images of the wheel, there are turned half-spokes of ivory between the wheel's black painted wooden spokes.