Please feel free to correct me if I am wrong. As long as I know karate was created in Okinawa but it's name was not karate, Giching Funakoshi was an okinawan sesei who sporticed and make karate available to the masses when he located in Japan (Tokio?) and began teaching in the universities there.
Karate in Okinawa was known under many different names, such as Te, Kempo, etc. "Karate", or more specifically "Karatejutsu" was the japanese pronunciation of the Okinawan term "Toudejutsu", which is pronounced Karatejitsu in Japanese and Tang Soo Sul in Korean. Later, they changed the front and back characters to Karatedo, Kara the character for empty, and do which means road, way or whatever.
Giching Funakoshi was in some way influenced by Dr. Jigoro Kano to create Karate Do?
Funakoshi Sensei adopted Judo's uniform and belt ranking system from Judo in order to transform Okinawan Karate into the competition oriented martial arts in Japan at the time, Judo and Kendo.
Persons like Mas Oyama and Gen Choi (The father of TKD) where pupils of Funakoshi, however there is no record I know about Gen.Choi been a directa student from sensei Funakoshi, some sourses say Gen. Choi got a second dan black belt under Funakoshi and became a chief instructor but I am not su sure.
Oyama Sensei claims to have learned at the Shotokan up to the 2nd Dan rank. Chung Do Kwan founder GM LEE Won Kuk stated that Oyama Sensei would visit Korea after WWII ended and would try to watch classes at the Chung Do Kwan. GM Lee stated that he used to chase Oyama Sensei away, and Oyama Sensei would come back and watch classes through the window. All of the original Chung Do Kwan students from the 1940's era knew Oyama Sensei because of his frequent visits to the Chung Do Kwan.
General Choi claims 2nd Dan rank in Karate; however, GM LEE Won Kuk and others dispute this and say that General Choi studied karate for less than one year while a student at Chuo University before he flunked out and voluntarily joined the Japanese Army. Back then, if you had any college courses, the Japanese Army would make you an officer, which is the route General Choi took. GM Lee and others who knew him in Korea during the 1940's and beyond state that General Choi had about a green belt level of knowledge when he came back to Korea after WWII, and did not study seriously while in Korea because of his military duties. General Choi became serious about it only after he was forced to resign from the Korean Army and exiled by President PARK Chung Hee to Malaysia as ROK ambassador to that country.