The main difference is:
A large Pushball will be kicked by the horse itself. And a Horseball is an small ball with leather handles, which will be catched by the rider. And a high basket, like basket ball, as an goal.
This year there will be a Premium in the Netherlands: Hélène de Fremery arranged that both equine games will give a show togehter on one day. On an international Driving Contest! It will be the World Championships Four-In-Hand on the Estate Heerlijkheid Mariënwaerdt of Family Van Verschuer in Beesd (NL): on Sunday 7th of September 2008. Watch http://www.wkvierspannen.nl/ (also English version).