This is a simple video demonstrating the actions of the O-ring and Western Dee. These are direct-action bits with no leverage and no mechanical advantage to provide amplification of force. They work on the tongue, bars, and lips of the horse, stretching the latter back as the rein pressure is applied. Thus, the cheek pieces of the bridle will be loosened as the bit is raised, and in extreme circumstances, the bridle can even fall off of the horse's head if it is not well-secured. Therefore, it is always advisable to use a headstall with a throatlatch when riding with a snaffle bit.
The loose ring bit has rings that slide freely, as its name suggests. This allows slight "jingles" of the reins to be felt more easily by the horse, which can allow for subtler cuing, but some horses do not appreciate the "noisiness" of this bit. Also, there is some risk of pinching if the lip gets caught between the cannons and the cheeks. The fixed ring bit is more stable in the mouth, and in addition, its flat sides push against the outside cheek and provide some outside lateral pressure when the horse is asked to turn to the side.
These particular bits both have a two-piece jointed mouth. The O-ring has a twisted mouthpiece, making it more severe as it rubs against sensitive tissue. These single-broken mouthpieces will fold in half as the reins are pulled, collapsing onto the tongue and bars. It has long been said that there is a "nutcracker" effect, where the middle point of the bit pokes into the horse's delicate palate. However, it has been shown by Dr. Hilary Clayton's research team that this effect is much exaggerated, and most horses will more than compensate by retracting their tongues, so that the palate is never contacted.