It is possible to have contact without a real connection (in fact it is quite common, unfortunately), but a true connection always involves good contact. The connection involves the horse's entire body… with energy created in the horse's hind legs traveling through the horse's supple body, and into the rider's hands.
In the sport of Eventing, ensuring that our horses are truly fit for our level of competition is one of the best ways to prevent unnecessary injuries.
Horses become incapable of learning when they go past a certain level of fear, anxiety, or stress. This means that if you keep hammering away at the horse, trying to teach them something when they are currently overwhelmed with stress, it will not work.
For the horse, the learning happens on the release of the aid. That means if you don't release the aid, the horse will not learn.
"Don't take the tempo down without revving the engine." ~ Chris Bartle