A crop consists of a long shaft, usually of cane (originally whale bone) which is covered in leather. One end forms a handle and the other a leather tongue, known as a keeper. A crop is relatively short, whereas a whip is a more common term that includes both riding crops as well as longer types of horse whips used for both riding and ground work.
A crop is not designed for use on the horse, but instead is used as in opening and shutting gates without dismounting, as well as a long leather thong attached to the keeper, which is used by whippers-in or hunt staff to rate hounds or by the field to keep hounds away from the horse’s legs, and possibly getting kicked.
The hunt crop show, without a thong yet attached, is from Laurent Sainsot, which features a piece of cholla found in Colorado and then taken home to France and made into a hunting crop with a stag horn handle.