Goju Ryu = the original Okinawan style Goju Kai = the Japanese version popularised / founded by Gogen "the Cat" Yamaguchi
Goju Kai tends to be a bit harder (i.e more emphasis on hard hitting). They are both good though, I have studied both Goju Kai 1 year (yellow belt) Goju Ryu 4 years (Brown Belt) The most important thing with any style is the instructor you choose. Dale
Usually when you say that you train in Goju Kai, you're affiliated with the I.K.G.A., as I was. If you're in Canada (especially in Ontario) and say that you train in Goju-Ryu, you might as well say that you're Canadian Goju-Ryu, as the style of karate around here has been greatly influenced by Bob Degleish. Goju Dale, who was/is your instructor? I might know him/her.
Goju Ryu is the form or style of Karate that we all practice, while the Goju Kai is an association within that style. However, because the Goju Kai became so prevelant in Japan, Goju Kai karate and Japanese Goju became synonomous. There are differences however. For example, it was in Japan where Karate began to be taught in schools and universities. This meant that class sizes increased significantly. As a result, greater emphasis was placed on line-up work and Kihon. Generally speaking this remains true and you will see more formal (militaristic) Kihon structures in the Japanese schools. Also, karate training moved more onto solid floors in Japan and the grappling and groundfighting elements were much reduced or even lost. Again you will generally find a greater emphasis on grappling in the Okinawan schools. It is for these reasons that many Okinawan practitioners view Morio Higaonna's Goju as more Japanese than Okinawan. However, as I said at the start, it's not quite so simple and Leo Lipinski once told me that many of the Okinawan Dojo, (including the Jundokan although I would need this one confirmed), once belonged to the Goju Kai. Also, people talk about the martial arts coming from China, through Okinawa and into Japan as though it were a linear thing. This concept completely ignores the return path and if you look at Goju in Okinawa it is clear that it has been heavily influenced by the Japanese - Gi, dojo, belts, line-up, kihon emphasis etc. Having said all that, I think it is fair to say that to all intents and purposes Goju Ryu has now come to signify the Okinawan variant and Goju Kai the Japanese.