For new members, interested horse lovers, or people just curious of terminology

Pony: by Pony Club definition, any horse being ridden by a youth under 18. By standard definition, any
  horse under 14.2 hands tall. This has nothing to do with a horse's age.
Horse: equines 14.2 hands and taller. Also used in general for both horses and ponies.
Stallion: uncut male horse (can be used for breeding). They are not allowed at Pony Club mounts and should
  not be ridden by children under 18, as they are unpredictable and very strong.
Gelding: cut male who cannot be bred. They have more predictable personalities than mares and stallions
  and are preferred for children.
Mare: female horse. Mares are never fixed (or "spayed") so they can be used for breeding. These can be
  very good for children, but they do have mood swings during PMS and when they are in season.
Foal: baby horse. Girls are called "fillies" and boys are "colts". We require horses to be at least 5 for
  children to ride in mounted lessons or competitions.
Hand: used to measure a horse's height. One hand equals 4 inches. A 15 hand horse is 5 feet tall at the
  withers, which is the part where the back and the neck join in a hump.
Green: horse with limited training or experience. Not recommended for beginners.
Rating: exam testing the member's horse management and riding skills on the flat and over fences. The
  purpose of a rating is to measure and define an individual member’s current skill level and to recognize
  achievement. The local club uses the Standards of Proficiency as a basic guide or plan for their
  instructional programs.
D Rating: an introduction to the fun and challenge of riding, establishing safety habits and knowledge of the
  daily care of a pony and tack. The D rated member learns to ride independently, with control, maintaining
  a secure position at the walk, trot and canter and over low fences. All D ratings are awarded at the club
  level.
C Rating: members learning to become an active horseman, to care independently for a mount and tack and
  to understand the reasons for what he or she is doing. The C shows development towards a secure,
  independent seat, and increasing control and confidence in all phases of riding. The C-1 and C-2 ratings
  are awarded at the club level. The C+/C-3 is awarded at the National level.
HB Rating: covers Horse Management knowledge that demonstrates increasing knowledge and competence
  in the care and handling of horses. Awarded at the National leve.
B Rating: is for the active horseman and Pony Club member who is interested in acquiring further knowledge
  and proficiency in riding. The B is able to ride experienced mounts with confidence and control. The B
  should be able to ride and care for another person's experienced mount, maintaining proper mental and
  physical condition without undoing any of the mount's education. The B understands and is able to explain
  the reasons for what he or she is doing and to contribute to the education of younger Pony Club members.
HM/H/HA Rating: covers horse management, teaching and training. The HM/H/H-A has the knowledge,
  experience and maturity to evaluate and care for a mount's needs efficiently and in a variety of
  circumstances, and to teach riding and horse care to others.
A Rating: is the highest level. The A is able to ride mounts at various levels of schooling with judgment, tact
  and effectiveness; to train young mounts; and to retrain spoiled mounts.
Aids: anything that helps the rider give cues to the horse. Natural aids include the legs, seat, hands and
  voice. Artificial aids include whips, spurs, martingales, or crops.
Dressage: classical riding style invented by Napoleon of France. Training of the horse in a ballet style.
Show Jumping: timed event over a set course of jumps.
Cross Country: riding in the open jumping over natural obstacles such as logs and hay bales.
Eventing: sport combining a dressage test, a stadium jumping round, and a cross country round, with scores
  combined. Most events take place over two to three days.
Tetrathlon: sport combining 4 separate events: riding, running, swimming, and shooting. The riding
  component is a show jumping course with some differences. The other events do not include horses.
Pentathlon: Olympic sport that is similar to tetrathalon but also includes fencing.
Vaulting: gymnastic event on horseback. Horse is lunged from the ground while vaulters perform on its back.
Quiz: pony club event without riding, based entirely on knowledge. Teams go to different stations which each
  test a different element of horse knowledge. Regional and national competitions.
Foxhunting: a non-competitive Pony Club sport
HM: horse management. Pony club term for the care, knowledge, and science surrounding horses. Important
  part of the curriculum at rallies and ratings.
Rally: pony club competition. Team event with traditionally 4 riders and 1 stable manager. Scores are
  combined between all riders as well as horse management scores, except in quiz, where there is no riding
  portion and is only scored on knowledge tested, and tetrathlon where scores are for individuals combining
  their riding, horse management, swimming, shooting, and running scores. Tet and quiz do not have stable
  managers. These competitions offer an oportunity to practice what they have learned and implement it on
  a team level.