Ryukyuan martial arts were not a monolithic entity called “toudi”, any more than there is one martial art in China called “kung fu” (or more precisely, “quan fa”). There were two major schools of Ryukyuan martial arts; one based in the capital city (Shuri-te) and one based in the major port (Naha-te).* “Toudi”, or more commonly “tote”, is Uchina Guchi (native Okinawan language) equivalent of quan fa (Mandarin) or Kempo (Japanese). ** It is a generic descriptor of multiple styles. It should also be noted that these earlier systems were true martial arts, and not the modern sports derived from them: that is, they were weapon-based, with unarmed combat a secondary consideration.
Ryukyu was repeatedly conquered by Japanese forces over its history, and gradually assimilated Japanese language and culture. The Okinawa “to-te” was gradually replaced with the Japanese “Kara-te”, written with the characters meaning “China hand.” During this period, unarmed combat and improvised weapons also became more significant in training, due to the Japanese prohibition on weapons. Naha-Te also divided into two schools, which are today called “Goju Ryu” and “Uechi Ryu”.
After World War II, Ryukyu voluntarily repatriated to Japan as the Prefecture of Okinawa. A council of karate masters, not wanting to show disloyalty to their new nation, decided that the name “Kara-Te” would be kept, but the characters would be changed from “China hand” to “empty hand”. This also helped with the concern of appearing overly-belligerent in post-War Japan, as they removed the weapons curriculum entirely, forming a different art called “kobujutsu” (literally, “the old way of fighting”).
Today, there are a mix of schools on Okinawa which teach the more traditional karate-jutsu/kobujutsu, and those who have adopted Funakoshi’s “-do” philosophy.
*Today, Shuri is a neighborhood in Naha, and the capitol is Okinawa-shi, a bit farther north.
**This does not mean “fist law”. That is some nonsense Ed Parker made up to sell books. It means “fist technique”.