The Spaniards brought the riding style (Vaquero) in the new world, where it developed further to today's western riding.
This type of riding is needed to drive cattle, so it's a working riding style. It is still practiced today in the US, South America and Australia.

Horsemanship (freely translated: "horse-human partnership") refers to the art of dealing with horses, of course. The horse should be handled and communicated in a natural way. In practical terms this means that the rider should correctly "read" the body language of the horse and understand that the horse accepts the rider's leadership skills. This applies to riding as well as to ground work. Here, the horse should neither be overwhelmed nor fed him pain or fear.