Henry Seishiro Okazaki immigrated to Hawaii from Japan. He learned 3 styles of Japanese Jujitsu while in Hawaii from Japanese Jujitsu Masters there. He went back to Japan and studied at many different locations, including with Jigoro Kano. Back in Hawaii, he trained Hawaiian Lua and Kung Fu.
Okazaki created Danzan Ryu with a base of Japanese Jujitsu, but adding in Lua and some Kung Fu.
One of Okazaki's students was Wally Jay. Wally Jay got his black belt from Okazaki and moved to California. He adapted what he learned, focusing a lot on small joint manipulation, creating Small Circle Jujitsu.
This is how the three are related.... Small Circle came from Danzan Ryu which came from Japanese Jujitsu and other things (Lua being the main other thing).
Modern Japanese Jujitsus, Danzan Ryu and Small Circle are great arts.... but the quality and flavor will vary school to school. Some are very much "do the kata, feel good, might as well be partner yoga." Some are very close to what you want, hard core kill each other every night at class. Most fall in between, some focusing more on kata form, others more on application and some trying to get into grappling / Judo competition.
The nice thing about Judo and BJJ is you pretty much know what you are going to get. They are pretty standardized. These other three... you have to go to the school in question and see.... They are not very standardized at all. Some are very good.... some would have trouble with a wet paper bag in a white belt.
