Pelhams and Kimblewick Bits are part of the leverage or Curb bit group which has a wide range of variation in design. Curb bits apply pressure across the lower jaw, tongue, poll and the curb groove to act on the nerve which runs under the jaw to encourage a horse to have a lower head carriage as well as maintaining the position of the bit in the mouth, especially important with ported mouthpieces.
The Kimblewick is generally considered a milder than a Pelham as it can not exert as much leverage due to the short shank design and is commonly used for riding as well as carriage driving. The Uttoxeter Kimblewick design allows different rein positions for differing leverage.
The Pelham design offers a muted but similar effect to a combination of Bradoon and Weymouth in a double bridle when ridden with two reins but doesn't take up as much space in a horse's mouth. The two-bit combination of a double bridle gives clearer signals through the reins than a Pelham though. Sometimes especially during cross country, a rider may decide to use a rounding so that they only have one rein, this uses both the snaffle and curb actions at the same time.