Cart Ponies: Cart ponies are ponies that are used to pull carts, sulkies, etc. Cart ponies can be two or four legged and can have fancy carts and tack like show ponies. Here I am specifically discussing a cart pulled by a single pony. There are also multiple pony carting teams, but I treat those separately since there are some important differences between single and multiple pony cart pulling.
Riding Ponies: Riding ponies are ponygirls or ponyboys who are ridden by their Riders (or Trainers/Owners/etc). Two legged and four legged riding ponies are both quite common. Generally, riding ponies have to be able to support their rider's weight. However, there is a fair amount of "simulated" riding in ponyplay. That is, the rider will support some or all of their own weight and will move in sync with the pony. Simulated riding is most commonly seen with four legged ponies.
Show Ponies: In ponyplay, the term "show pony" does not exclusively refer to a pony that is trained and taken to shows. Rather, a show pony is often a catchall term that differentiates "working" ponies (i.e. riding and cart ponies) from other ponies. Of course, this is not to say that show ponies do not have to expend effort. Many show ponies have intense training regimens including a lot of work on the lounge line. Moreover, a show pony may have extensive training in dressage and jumping, both of which are demanding and strenuous activities.
In pony play, you will find that many people may use the term "show pony" to be synonymous with "dressage pony". This is usually done for simplicity since many show ponies are dressage ponies. However, not all show ponies are trained in dressage. Indeed, some show ponies are shown in halter, or to display their tack.
Rubber Ponies: Rubber ponies have equipment fashioned from rubber. Indeed, rubber ponies will often be totally encased in rubber: a rubber (often rubber latex) catsuit, rubber pony mask covering the head, rubber fist hooves, rubber bit, etc. The rubber pony combines the pony play fetish with the rubber fetish. While exclusive rubber ponies exist (i.e they are just rubber ponies), most rubber ponies are invlved in another aspect of ponyplay (e.g. carting, riding, etc.).
Dressage Ponies: Dressage ponies are usually considered to be show ponies that are specifically trained in dressage. Dressage ponies will be able to perform advanced movements. Moreover, in ponyplay, dressage ponies, like show ponies, often be very well groomed and have fancy tack. Some ponies will be cross trained in dressage along with another discipline either in preparation for eventing, because dressage training will assist the pony in the other discipline(s), or simply because the pony and/or trainer enjoys dressage.
Eventing Ponies: Eventing ponies are considered to be sub-type of show ponies. In ponyplay, a show pony is not necessarily a pony that is taken to shows. Indeed, in ponyplay the term show pony is often used merely to differentiate "working" ponies (i.e. riding and cart ponies) from other ponies.
Working Ponies/Horses: Working ponies/horses are also referred to as draft ponies/horses, pack ponies/horses. While all ponies need to have some athletic ability to carry a rider, pull a cart or show off their gaits, working ponies are trained specifically for athletic ability. Working ponygirls or ponyboys are trained to pull heavy loads over longer distances and over rough and terrain and obstacle courses. The working pony is trained just like a real work horse, and can pull loads of rock, wood, etc. Working ponies can also be used to move heavy objects blocking paths and trails, such as branches or small trees. These ponies typically have utilitarian tack and are very much about function instead of appearance. Working ponies are also trained to work blindfolded, and there are working pony shows where the ponies will pull a heavy load through an obstacle course while blindfolded. In addition to testing athletic ability, this type of show also tests how well a pony can interpret non-visual cues, and how sensitive a pony is to the aids (such as the reins).
Breeding Ponies: Breeding ponies are ponies that are, well, meant to be bred. Breeding ponies breed with other ponies; this can involve actual sex, or it can simulate breeding. Breeding scenes, especially those involving actual sex are agreed upon by the ponies involved prior to entering pony role.
Pleasure Ponies: Pleasure ponies are ponies that are there to pleasure their owners and trainers. Pleasure ponies are sometimes referred to as "pony slaves" or, less commonly (likely due to confusion with the device of the same name), "bondage horses". The difference between breeding ponies and pleasure ponies is that breeding ponies are there to "breed" with other ponies, while pleasure ponies are there for the pleasure of their trainers and owners, and not of other ponies specifically. One could argue that most ponies are pleasure ponies in ponyplay since this is why many of us engage in ponyplay to begin with.
Bondage Pony: Bondage ponies are focused exclusively, or nearly so, on the bondage aspects of ponyplay. Nearly every form of ponyplay contains some aspect of bondage, which adds to the whole experience. The involvement of bondage in ponyplay can vary significantly, but nearly always, bondage is just one element contributing to a scene. However, for the bondage pony, the physical restraint is the primarly driving force for engaing in ponyplay.
Multiple Pony (Team) Carting: While similar to cart ponies in many ways, ponies that are trained and work as team to pull carts must have a significant amount of additional specicialized training beyond that of other cart ponies. Cart ponies that work as team are nearly always two legged ponies, and almost always have matching, aesthetically pleasing tack. Moreover, the ponies that make up a team are usually chosen to of similar height and overall physcial build. There are very few (to my current knowledge) multiple pony cart teams in ponyplay. This is most likely due to the difficulty not merely in finding multiple ponies, but in the regular group training required to facilitate safe and smooth operation of working together. However, it is quite a sight to see human ponies working together pulling a cart.
Found on: http://www.cpony.com/home/ponies/