Dai and Shō in Kata
Some karate kata have Dai (大, big) or Shō (小, small) in their names. For example, Kusankū Dai and Kusankū Shō, or Passai Dai and Passai Shō.
Now, as to the meaning of these Dai and Shō, it is generally believed that Itosu Ankō modified the koryū (i.e., pre-Itosu) kata and called the pre-modified kata “Dai” and the modified kata “Shō.” So, Kūsankū Dai and Passai Dai are the kata that existed in the old style Shuri-te, while Kūsankū Shō and Passai Shō are the kata that Itosu Sensei modified.
Historically, only Kūsankū and Passai were distinguished from Dai and Shō before World War II. For example, Funakoshi Gichin wrote the following in Ryukyu Kenpō Karate (1922).
There are five types of Pinan and three types of Naihanchi as the current popular te (hands). Passai is divided into two types, Dai and Shō, Kūshankū also has two types, Dai and Shō, and all the others have one type each. (Note)
Therefore, the other kata with Dai and Shō are mainly postwar creations or newly renamed kata. For example, in the Shōtōkan lineage, there are kata named Gojūshiho Dai and Gojūshiho Shō, which were probably named after the war. In recent years, other kata with the name “Dai” have also appeared, but they seem to be basically created kata.
However, in Kobayashi-ryū, Chibana Chōshin called Tawada’s Passai as Passai Dai, so…