What is the difference between Ahlul Hadith(People of Hadith) and Ahlul Rai(People of opinion) from fiqh perspective in the sense how do they differ in ruling? , I read that Hanafi Madhab is the only school which subscribes to Ahlul Rai is that true? and how is such an AhlulRay madhab different from the Ahlul Hadith Madhabs like Shaafi, Hanbali, Salafi etc, in the manner of deriving rulings?
From a juristic perspective, the ahl-ul ra'y are so-called because of their practice of juristic preference, which is to say the practice of choosing one evidence over another based on personal (some would say arbitrary) preference rather than on the strengths thereof.
Two major examples of this would be the Hanafi principle of istihsan and the Maliki principle of istislah, both of which applied evidence based on how suitable the jurist felt they were rather than on their relative strengths. As such, strong evidences could be ignored in favour of weaker ones — or even personal opinions — when the jurist felt it necessary.
In simple terms, it could be said that ahl-ul ra'y attempt to apply the spirit of the law in their rulings where ahl-ul hadith would instead apply the letter of the law.