Hi Jocelyne, I think Centred Riding is the same as GOOD traditional riding of any discipline. That is, the rider is balanced and has an independent seat, and is riding from her core, with clear intention and light cues. Doesn't matter whether you're riding English, Classical, Western.. Bareback.. the same basic principles apply.
The difference is in the WAY that Sally Swift teaches it. Because of her own battles with scoliosis when she was young, she had to learn to understand the movement of her own body very well.. and she took horseriding lessons in order to help straighten herself. She then sharpened what she learnt during that time during her whole lifetime, so she has a wonderful ability to put the concepts of good riding into language that anyone can understand and use - something very few of even the best riders can do, because most are doing it naturally, without thought. She mostly uses analogy and visualisation to help riders get their bodies working effectively for them. I use lots of her teaching ideas when I'm coaching, with great success. I have a few clients who've been having lessons for years in traditional stables, but in just a few sessions I can help them to feel very much more comfortable and effective in what they do on a horse.
I highly recommend you get her books and DVD, whatever sort of riding you want to do.
I have not sought the horse of bits, bridles, saddles and shackles,
But the horse of the wind, the horse of freedom, the horse of the dream. [Robert Vavra]