A noseband is the part of a horse's bridle that encircles the nose and jaw of the horse. In English riding, where the noseband is separately attached to its own headstall or crownpiece, held independently of the bit, it is often called a cavesson or caveson noseband. In other styles of riding, a simple noseband is sometimes attached directly to the same headstall as the bit.
Parade horse regalia, showing a noseband attached to a bridle, an example of a noseband used primarily for style, though it also is the point of attachment for a standing martingale.
Classic English-style Cavesson Noseband
Flash noseband
Figure-eight noseband.
A bridle is a piece of equipment used to direct a horse. As defined in the Oxford English Dictionary, the "bridle" includes both the headstall that holds a bit that goes in the mouth of a horse, and the reins that are attached to the bit. It provides additional control and communication through rein pressure.
A hunt seat style English bridle
Western show bridle
The crownpiece runs over the horse's poll, and the browband across the forehead. The cheekpieces run down the sides of the horse's face.
A double bridle, using two bits