The cricket is made of steel and has an uneven center hole that is mounted on a square center bar. This creates a cricket sound when the horse rolls it with his tongue. The more motion the horse has with his tongue the more relaxed the lower jaw is. The relaxation of the lower jaw helps keep the lateral bend in the neck and also helps keep the motion of the front legs.
The cricket allows the rider to listen to their horses. Some horses roll the cricket when relaxed and soft while other horses will aggressively roll the cricket when nervous.
The roller is made of copper and has a round center hole that is mounted on a round center bar, this allows the roller to roll without much noise. The roller still encourages the lower jaw to relax and create saliva similar to the cricket.
Both the cricket and roller have the same dimensions so the mechanical effects are the same.
All three piece mouthpieces and chain mouthpieces have the option of a cricket or roller.
Pictured here the CRICKET (top) and the ROLLER (bottom). Notice the color difference as this is the easiest way to identify between the two in an image. The roller is always a brass color, the cricket is always silver.