While both breeding and pleasure ponies are often for used for sex, breeding ponies have sex with other ponies and pleasure ponies are used for the sexual pleasure of their owners/trainers. You may sometimes hear pleasure ponies termed "pony slaves". However, since "pony slave" can also generally refer to any bottom forced into ponyplay, I find this term to be misleading.
Note: There might be some confusion here with the bio-equine term "pleasure horse" which is applied to bio-horses that are used for general riding/hacking. I am not referring to this type of pony.
Many ponies are used by their owners/trainers for sexual pleasure, so this type of pony is particularly difficult to define well. However, I would consider a pleasure pony to be one who engages in ponyplay (or at the very least, a particular ponyplay scene) specifically to be used in a similar manner to a bondage sex slave in (non-ponyplay) BDSM. The separating factors between the two being the pleasure pony will be dressed and behave (or forced to behave) like a horse. Moreover, the pony will be treated as an animal versus a human slave.