This style comes from the teachings of Kanken Toyama. Toyama was an Okinawan educator and karate headmaster. He was a student of both Ankoh Itosu (of Shuri-te) and Kanryo Higaonna (of Naha-te). He mastered both systems and he taught both systems as complete martial arts.
After the war, Toyama came under the direction of his three senior peers. He received instruction first from Chojun Miyagi, and the Choshin Chibana. After the death of Miyagi in 1953, Toyama received instruction from Jyuhatsu Kyoda of Okinawa Toon-ryu.
The name, Okinawa Seito Karate-do, comes from Toyama's teachings in that he taught both systems -- both complete systems. First you must learn all the old Shuri-te forms before you are indoctrinated into the advanced Naha-te methods. So it is like first learning all of the teachings of shorin-ryu and advancing to the goju-ryu system. Both are complete martial arts and both compliment each other.
To pay respect to both systems, Toyama adopted the name Okinawa Seito Karate-do (Okinawa Orthodox Karate-do). This means he was teaching all of the methods of Shuri-te and Naha-te. In technique, he merged both systems but left the kata pure. The only exception was in the kata sanchin. Miyagi performed the kata with his hands closed but Kyoda corrected the form so it was done with the hands opened.
the following Shuri Kata: Pinan 1 through 5, Naifunchin shodan, Bassai-dai,
Chinto, Chibana Kusanku-dai and Okugi Gojushiho.
This is followed by our advanced kata: Naifunchin nidan and sandan, Wankan, Shuri Seisan, Jion, and Shuri Sanchin.
While completing the Shuri kata you are also indoctrinated into the Nintan-ryu Bojutsu.
After completion of the Shuri kata you are taught the advanced forms of Goju-ryu/toon-ryu.
the following Bojitsu kata: tenryu-no-kon, shushi-no-kon, sakugawa-no-kon,
yonegawa-no-kon, sunagake-no-kon,hakuson-no-kon, tsuken-bo, teruya-no-kon,
oshiro-no-kon, and Chibana-no-kon.
The last one is in honor of Toyama's senior, Choshin Chibana of Okinawa. It should stated that Chibana's shorin-ryu kata and Toyama's kata are virtually the same in translation.