Max Gahwyler was known for his deep understanding of dressage and its history. Here's a quote from The Competitive Edge.
" Where is the common denominator between the past [ la Gueriniere and dressage as practiced at the Spanish Riding School] and present? It lies in the basic training of the horse, up to about our Third or Fourth Level, where the horse learns to move forward, to be straight, supple, balanced, light in front, and on the bit. The methods we use to achieve this - shoulder-in, travers, renvers, simple changes, half passes, smaller and smaller circles, circles on two tracks, rein backs, and so on - are nothing more than schooling exercises and were called the Campaign School [ cavalry term ]. "
BTW, the true Haute Ecole movements were left out of the modern dressage tests because they weren't suitable for the military horse of the day. "The emphasis [of Haute Ecole] was always on collection and execution of the individual movements [ a long list only 3 of which are included in the modern Grand Prix test ] done to perfection, rather than a sequence of movements done in the modern dressage test. "
The modern dressage test emphasizes the ability of the horse to always go forward without interruption or loss of balance, which is why the transitions become so important. Not a requirement of Classical = Baroque dressage which is totally about riding in collection.
The goal of Western Dressage is that expressed by every writer on dressage I can find - to create harmony and relaxation between horse and rider using a system of exercises (see above) that lead to a horse that is straight, forward, and calm. It's that system of exercises that distinguishes dressage training from anything else.