They consist of a cutting wheel attached to a handle. The wheel will have a sharp edge. The edge may be plain, and meant just for plain no-nonsense cutting, or it make have a jiggety edge (usually wavy), making it a combo pastry wheel / pastry jigger to give the cut a decorative effect.
Technically, if there is a decorative edge, then the device is a pastry jigger, but that term is being lost and blended into Pastry Wheel.
Pastry Wheels will vary in size. The larger ones can be used for slicing cooked pizza.
Some Pastry Wheels have interchangeable wheels, including a plain edge and some jigging edges. Some have dual wheels attached to the handle: a plain edge wheel to the left, a decorative edge wheel to the right. Which one you use depends on how you turn and angle the device.