Well, not necessarily. San Da and San Shou are both terms that basically mean the same thing. Fighting or sparring with various techniques including striking using the arms and legs as well as grappling.
San Soo is a form of Kung Fu that was proliferated in Western US but I have little doubt that it originally was making reference to San Shou. Perhaps San Soo is just a westernization of the term but it became systemitized, complete with forms or at least "lessons" which I think the now deceased grandmaster put together to teach it similar to the Jiu Jitsu or Karate that was prevalent at the time. He even called the lessons, "jujitsus".
It is not a sport and they emphasize that it is for self defense ONLY! It's reported that the guy who teaches that super effective modern self defense system, SCARS is a black belt of San Soo Kung Fu.