To answer your question from a previous page; none of the three horses you posted photos and vids of are collected.
The dressage video is of an event horse doing a First Level test; collection starts at second level. That horse is not a great example of the terms we're discussing.
In the photo of the western horse loping; that horse is connected back to front and moving from his hind end, but not collected.
True collection in the dressage sense feels like a sports care revved up to the redline but with the clutch in. You know if you let that clutch out a lot of energy is going to escape.
To try to answer some of your other questions; a horse doesn't have to have lots of overtrack to be considered engaged. I use engagement to mean how far under the horse's body the hind end comes before striking the ground and pushing off. Some people use engagement simply to mean that the horse is working from the hind end, and that the hind end is active. Not right or wrong, just a different meaning depending on context.
Additionally, with horses that jump, you'll hear trainers refer to "engaging evenly" - this means that when the horse pushs off to jump, the hind feet are together and pushing off at the same time. A horse that doesn't engage evenly, and leaves one hind leg back, as in the canter stride, can't jump as athletically because there's less "push." It's a heavily penalized fault in hunters.
Overtracking is desirable in hunters because it means a ground covering stride.
Overtracking is desirable in dressage horses because as you move through the levels and work on collected paces and advanced movements, you will lose some of that reach under the body. If you start with a horse with lots of overtrack at the lower levels, you'll still have adequate engagement in the collected paces and advanced movements. If you start with a horse that barely tracks up, and then lose some degree of engagement as you move up, the collected paces/advanced movements will be very hard to achieve, weak or incorrect as the hind end won't be fully under the horse.
A final note - if you only understand and use terms as they apply inside your discipline, that's fine. However, if you're interested in becoming an educated or well rounded horseperson, it's great to understand what the terms mean in their original sense and how they're used in other disciplines. That doesn't mean someone else is wrong when they refer to a WP horse as collected; it just means that they mean it in a limited, discipline specific sense.
Last edited by maura; 06-20-2010 at 10:18 AM.