Modern history of East Asian martial arts
Taekwondo was developed from karate for use in the Republic of Korea Armed Forces from 1954. For this purpose, karate terminology needed to be "nationalized". The name "taekwondo" is due to shotokan practitioner and army general Choi Hong Hi. After the Korean War, Taekwondo was further developed into a purely sportive discipline, since 1973 overseen by the World Taekwondo Federation. 
During 1964-1966, Choi Hong Hi continued to promote taekwondo, working to put together a world-class exhibition team. Taekwondo's emphasis on jumping and flying kicks dates to this period. While taekwondo was based off karate, the structural changes made in the 1950s and 1960s were significant, and it cannot now be considered a branch of karate, but is a standalone modern martial art. Taekwondo was presented at the Summer Olympics as a demonstration sport in 1988 and 1992, and became an official Olympic discipline in 2000.
Taekwondo
After witnessing a martial arts demonstration by the military in 1952, South Korean President Syngman Rhee urged that the martial arts styles of the kwans be merged. Beginning in 1955 the leaders of the kwans began discussing in earnest the possibility of creating a unified style of Korean martial arts. The name "Tae Soo Do" was used to describe this unified style. This name consists of the hanja "tae" "to stomp, trample", "su" "hand" and "do" "way, discipline".
Choi Hong Hi advocated the use of the name "Tae Kwon Do", i.e. replacing "su" "hand" by "kwon" (Revised Romanization: "gwon"; McCune–Reischauer: "kkwŏn") "fist", the term also used for "martial arts" in Chinese (pinyin "quán"). The new name was initially slow to catch on among the leaders of the kwans.
In 1959 the Korea Taekwondo Association (KTA) was established to facilitate the unification of Korean martial arts. In 1966, Choi broke with the KTA to establish the International Taekwon-Do Federation (ITF) - a separate governing body devoted to institutionalizing his own style of taekwondo.
Cold War politics of the 1960s and 1970s complicated the adoption of ITF-style taekwondo as a unified style, however. The South Korean government wished to avoid North Korean influence on the martial art. Conversely, ITF president Choi Hong Hi sought support for the martial art from all quarters, including North Korea. In response, in 1973 South Korea withdrew its support for the ITF. The ITF continued to function as an independent federation, then headquartered in Toronto, Ontario, Canada; Choi continued to develop the ITF-style, notably with the 1987 publication of his "Encyclopedia of Taekwondo". After Choi's retirement, the ITF split in 2001 and then again in 2002 to create three separate federations each of which continues to operate today under the same name.
In 1973 the South Korean government's Ministry of Culture, Sports and Tourism established the Kukkiwon as the new national academy for taekwondo. Kukkiwon now serves many of the functions previously served by the KTA, in terms of defining a government-sponsored unified style of taekwondo. In 1973 the KTA and Kukkiwon supported the establishment of the World Taekwondo Federation (WTF, renamed to World Taekwondo in 2017 due to confusion with the initialism) to promote taekwondo specifically as an international sport. WT competitions employ Kukkiwon-style taekwondo.
For this reason, Kukkiwon-style taekwondo is often referred to as WT-style taekwondo, sport-style taekwondo, or Olympic-style taekwondo, though in reality the style is defined by the Kukkiwon, not the WTF.