San identifies his style only as "Okinawan  Karate", but that could be any of the Okinawan styles that share  this form. Since in the Karate Kid Part II Miyagis Nemesis runs a  school in Naha with the Gojo Ryu fist as a logo and his students  wear the Gojo Ryu fist on their uniforms, then Miyagi is probably  teaching Gojo Ryu (one of the five main styles of Okinawan  karate)since Miyagis father taught both him and Sato.