Although the roots of Taekwondo and Hapkido are embedded within Japanese Karate, today, both are widely recognized as Korean martial arts. For Taekwondo, most commonly, the art was originally derived from Shotokan Karate with Hapkido origins founded upon Daito Ryu, originally known as Daito Ryu Aikijitsu. Still, both are very different from the other, yet each are commonly taught together throughout schools across the country.
There is, of course, a distinct separation between the two styles as each are still considered as a complete different system of martial art from the other. As Taekwondo and Hapkido are obviously individual arts in their own rights, it is interesting to note how both found their way into the integrating of martial arts.
To understand this, one must first focus on the founding of Hapkido. As one who's training has primarily been in Taekwondo with only various basics of Hapkido, I can only provide my personal view as it relates to this issue. Although a controversial topic even today, many consider Yong Sool Choi to be the founder of original Hapkido. More widely popularized, others look to Han Jae Ji as the founder.
Yong Sool Choi originally taught Daito Ryu. Later, he would integrate Judo into the Daito Ryu system. Choi referred to his self defense system as Dae Dong Ryu Yu Sool, which is the Korean term for Daito Ryu Jujitsu. This, I believe, would set in motion the beginning of the founding of what would become known as Hapkido. At this point in time, it seems clear that Choi's primary system was the Japanese martial art of Aikijitsu.
Having trained full-time under Yong Sool Choi in Taegu, South Korea for several years, Han Jae Ji would later relocate to Seoul in 1957 where he opened his own school. Between the years of 1957 and 1960, Ji began integrating various kicks and striking techniques that he took from other Korean schools. Because of this change in styles, Ji would note that his style was much different from the original style of Yong Sool Choi and would name his style: "Hapkido."
Han Jae Ji contacted Choi, sharing with him the newly founded name and Choi is known to have taught using the Hapkido name up until his death in 1986; however, Choi continued to remain true to his original teachings, withholding the kicking, striking and weapon techniques incorporated into the art by Ji. Therefore, because of this lineage of history, many see Yong Sool Choi as the "Father" of Hapkido and Han Jae Ji as the "Founder."
As founder of the original Korea Hapkido Association and Sin Moo Hapkido, Han Jae Ji, who Bruce Lee considered to be "the best fighter and marital artist in the world," is still very active in the promotion and teachings of Hapkido. On August 17, 2013 Dojunim Ji led a seminar presented by Grandmaster Troy Smith, founder of the Universal Hapkido Society. As in any martial art, new styles are conceived from previous foundations such as Grandmaster Smith's, Ko Shin Kwan Hapkido, which has become one of the top rated Hapkido schools in the State of Texas.
Another Hapkido school which should be noted as one of the "Best of the Best," is located in Marion County, Florida. The Florida Academy of Korean Martial Arts is operated by Master Fabian Duque, founder of Jung Sool Kwan Hapkido and President of the Korea Hapkido Jung Sool Kwan Association of Ocala, Florida. Master Duque teaches Hapkido, Taekwondo and Yong Moo Do, a new martial art developed by Yongin University which integrates many other arts such as Taekwondo, Judo, Kumdo, Hapkido and Ssirum.
Hapkido continues to be one of the most popular martial arts today and it is widely recognized that Han Jae Ji was the first to understand that by integrating the best of both arts, Hapkido and Taekwondo, would undoubtedly prove to be beneficial in the development of further martial art styles.