Funakoshi wrote in Karate Do Kyohan that back in the 1800s, it was common for a person of considerable skill to learn only a few kata, three was common. Motobu certainly believed in that. He probably was exposed to a number, but he taught only a few, and it is believed only practiced a few extensively.
Thanks to video of tournaments and demonstrations, we can look to youtube for a fairly robust inventory of Okinawan kata that have survived until today. Scores, certainly, have perished. But we have a visual record unimaginable in the days when a person was only exposed to a few.
Back in the 1800s, if you were taught Passai, or Gojushiho, or Kusanku, you were taught a single version. However, by the late 1800s, and certainly in the early 1900s, karateka began to gather the kata practiced by others. Chotoku Kyan is a good example. Sokon Matsumura taught him only Seisan and Gojushiho. And from other old karateka, he learned but a single kata from each.
Itosu, by the time he died, is believed to have passed on over 20 kata to Mabuni. Itosu clearly broke the old mold where one only learned but a few kata in one's lifetime. Probably because of his station in life, a clerk (an important position) in the Ryukyu government, and a leading student of Matsumura and Gusukuma, he was in a position to share and learn kata from other prominent karateka of his day.
What's important to note, is that we can look to youtube as a resource to better understand the variety of kata that have been handed down with common names. There are numerous versions of Passai (Bassai) and Kusanku. Itosu passed down two versions of each to his students. (At least to Mabuni and Chibana.) I would argue that the dai and sho terms were simply means to differentiate between two different kata of the same name.
It is generally recognized that dai refers to something bigger, and sho something smaller. Some argue that this refers to length, but I have my doubts. Rather I would argue that the dai may often carry the connotation of which is the more important of the two, or perhaps which is learned first.
It's been noted above, but the dai and sho terms are not uniform with Passai. Chibana's Passai sho is Mabuni/Funakoshi's Bassai dai. Chibana's Passai dai is also called Matsumura Passai by both Chibana schools as well as Mabuni schools. Chibana's Passai sho is refered to as Itosu Passai in Chibana schools, and Mabuni/Funakoshi's Bassai Sho, is referred to in at least some Chibana schools as Koryu which translates as "old or ancient way" much the way kobudu) (ICYMI, in Iha's schools this kata is also called Gusukumu Passai. My guess would be that this Gusukumu is the one mentioned in the Master Text as being Itosu's teacher.)
Hohan Soken also passed down two Passai kata, sho and dai. While the opening of his dai is unique, much of the rest maps closely to the Funakoshi/Mabuni Bassai Dai. Soken's Passai sho is unique to his system. Nakamura's Passai is unique. And certainly Kyan's Oyadamari Passai differs substantially enough to call it unique.
There are other less widely known versions out there as well.
Much the same can be said for Kusanku. There are many versions. I believe Itosu was the only one to pass down two, so he called them sho and dai.
There are some who might believe that we can trace the origins of these various versions of kata back in time. I don't believe that is possible. Virtually nothing written with that kind of detail survived.
I have seen numerous questions on this forum and elsewhere, that seek to understand the lineage of specific kata. Specifically, which is older, which descends from what, and especially, which is the "original" kata.
I do believe that we can benefit from comparative analysis of the members of the various kata families. We can learn what the similarities are and what the differences are. But it is unfortunate that we will never be able to determine how these various kata came to be. Is there an original from which modifications were made? We can never know. All we have are the kata.
Cayuga Karate