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.
Tae Soo Do
Today, the name Tae Soo Do is no longer used by Taekwondo practitioners or schools. Very few people who practice Taekwondo today will recognize the name except for its modern use with the Hwa Rang Do community. In the west, the art was always referred to as "Tae Kwon Do" (or "Taekwondo", the western form of the name), due to that the controversies that happened in Korea during the early 1960s never made their way over to the United States aside from a very select few, who chose to watch eastern culture and events closely in order to keep traditions alive and accurate.