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
In 1962 Jhoon Rhee relocated to the United States and established a chain of martial arts schools primarily in the Washington, D.C. area that practised traditional taekwondo. In the 1970s, at the urging of Choi Hong Hi, Rhee adopted ITF-style taekwondo within his chain of schools, but like the GTF later departed from the ITF due to the political controversies surrounding Choi and the ITF. Rhee went on to develop his own style of taekwondo called Jhoon Rhee-style taekwondo, incorporating elements of both traditional and ITF-style taekwondo as well as original elements. (Note that Jhoon Rhee-style taekwondo is distinct from the similarly named Rhee Taekwon-Do, based in Australia and New Zealand).