OK...I'll try to illuminate some of this for you. I conceed it can be a bit confusing because you have to wade through a whole lot of revisionist history and modern propoganda to arrive at what really is the truth.
Won Kuk Lee did not 'INVENT' Tang Soo Do. Neither did Hwang Kee. This misconception comes from the fact most westerners never study martial arts history in any detail and rarely ever take time to learn at the least the essential parts of the written language associated with Asian Martial arts...that being 'Chinese'. To erudiate...the Chinese written language was the only written language used by the various provinces of China as well as by the Japanese, the Koreans, the Okinawans, Tawainese and some of the South Sea countries such as Thailand, Viet Nam, Cambodia etc at various times. This worked well because while they may all have had different 'SPEAKING' languages, they could communicate through the written language which was Chinese in origin. Most officials of the various governments read Chinese even if they didn't speak it. Even today, Japan and Korea still maintain the usuage of about 1200 Chinese characters that can be used along side their own phonetic languages (hiragana in Japan/ hangul in korea). In Korea, the use of Chinese characters is known as 'Hanja'. This is important an you have to know it for you to grasp what follows.
In Hangul, Tang Soo Do is written: 당수도
In Hanja it is written: 唐手道
which translates as 'China Hand Way' literally. The character 唐 ( 당 ) is a reference to the 'Tang Dynasty' in ancient China and became synonymous with the advancement and identification with Chinese Martial Arts. When the Okinawans were learning martial arts from Chinese teachers, they refered to their art as 'Tode' which was their dialect for 唐手 . In Japanese this is pronounced 'Kara Te' . A legendary figure in Okinawan Martial Arts is Master Sakugawa who is said to have learned from the Chinese diplomate Ku Shan Kun (known in the Korean language as Kong Sang Koon) from whom he learned Chinese martial arts the Okinawans referred to as 'ToDe' or 'Tang Hands' to be differentiated from their native martial art simple referred to as 'Te' or 'Hands'. Because of this he was nicknamed 'Karate Sakugawa' and it from this event in history that we have the term 'Karate' ( 唐手 ) coined. When Okinawan Karate Master Ginchen Funakoshi and others took the Okinawan martial art to Japan, it was refered to as "Karate Do" ( 唐手道 ). However, due to the era of nationalism, they later adopted the character 空 which means 'Empty', which is actually pronounce 'Ku' in Japanese but they continued to pronouce it Kara which then gave us the interpretation of 'Karate Do' as 'Empy Hand Way'.
Now many Koreans did study in Japan (and I can't emphasize enough the need to study the history of the various nations of Asia around the era of WWII or else you will have gaps in your understanding of WHY things happened the way they did and WHY things are the way they are now), and many of these Koreans DID earn black belts per se in Karate Do (of one type or another). Some of them came back to Korea and opened schools after the end of WWII (1945). One such person was Won Kuk Lee. Actually, Lee had returned to Korea in the 1930's and did obtain permission from the Japanese authorities to open a 'Karate' school in Seoul. Mr. Lee had studied in Ginchen Funakoshi's school in Japan known as Shotokan. But in Lee's language, the art was not referred to as Karate Do, but as Tang Soo Do ( 당수도 ). This is because Lee returned to Korea and began teaching prior to 1935. I mention this, and it is important to your understanding because it wasn't until 1935 that the Japanese began to use the characters 空手道 or 'Empty Hand Way'. In hangul, these are pronounce as 'Kong Soo Do' ( 공수도 ).
Hwang Kee graduated from high school in Korea and took a job with the Rail Road. This afforded him the opportunity to travel throughout Korea, Manchuria and into at least northern China. During his travels, he met a master he referred to as Yang Jin Kuk from whom he learned Yang style Tai Chi Chuan. He studied with Mr. Yang for only about a year and half then his job returned him to Korea in late 1937. He then began to work for the survey branch, Railway Division of the Ministry of Transportation. As a result of this, next to his office was a library which contained several books in Japanese on Okinawan Karate. While Hwang Kee never provided a list of what books he had access to, we now assume one was Ginchen Funakoshi's book 'Tode-jitsu' (reprented recently in English under the title 'Karate Jutsu'). Following the end of WWII and Korea's independence from Japanese authority, Hwang Kee attempted to open his own martial art school based upon what he had learned which he called the 'Moo Duk Kwan' and he referred to his art as 'Hwa Soo Do'. However, on two consecutive attempts to form classes, they both failed within 6 months of starting. Then in early 1947 he happenned to run into Mr. Lee and another Korea who had studied in Japan, Mr. Chun Sang Sup. Won Kuk Lee ran the 'Chung Do Kwan', Chun Sang Sup ran the 'Yun Moo Kwan' (later renamed the 'Ji Do Kwan'). From this meeting he struck up a friendship. Lee invited Hwang Kee to come work out at his school and Hwang Kee took him up on this offer. We know he worked out at the Chung Do Kwan for about 6 months. Mr. Chun and Mr. Lee both advised Hwang Kee that the reason he was having trouble forming a school was because his 'Hwa Soo Do' was too alien to Koreans after their 40 years under Japanese domination. They were used to Japanese things such as Karate. This was when Hwang Kee decided to start using the 'Karate' patterns which you see Tang Soo Do practitioners using today. Now during his time training with Lee Won Kuk, Hwang Kee did have a problem with Lee's senior student, Son Duk Sun. The word is Son got very ticked at Hwang Kee because HE felt Hwang Kee was being disloyal to Lee by not becoming a FULL Chung Do Kwan member and giving up his goal of opening his own school. It has been rumoured that they fought and Hwang Kee lost...however...this was never substantiated. What probably happenned is they had a bad verbal argument. Nonetheless, Hwang Kee did stop training at the Chung Do Kwan and did reopen his Moo Duk Kwan in late 1947. This time...because he was teaching 'Karate' forms, he was successful. Hwang Kee maintained a decent relationship with both Lee and Chun for years afterwards. Because of this, many of us believe that Son's real motivations behind his dislike of Hwang Kee may have been jealousy at Lee allowing Hwang Kee access to the Chung Do Kwan and treating him like a peer. Where this gets complicated is the comments Lee Won Kuk has made in the last decade such as that Hwang Kee was his student. However, you have to take that with a grain of salt as Lee is very old now....and according to him....everyone of significance in Korean Martial Arts has been his student. The story about Hwang Kee being a 'Green Belt' in Lee's school is pure modern propoganda as they didn't start using these belt ranks until post the Korea War (after 1953) and this was because they noted the adoption of color belt system by Japanese martial artists.
By now you should have figured out that Tang Soo Do, Karate Do, 唐手道 , and 당수도 are just different ways of writing the same thing. And that it was not INVENTED by anyone...but merely a generic reference to Martial Arts which in actually have a 'Chinese' ancestry at some point. The respective ARTS founded by Lee Won Kuk and Hwang Kee were the 'Chung Do Kwan' and the 'Moo Duk Kwan' and each are distinctive interpretations of 'Tang Soo Do'.
So don't let anyone fool you....Lee Won Kuk didn't anymore INVENT Tang Soo Do than did Hwang Kee or anyone else for that matter. They didn't even 'coin' the term.
I hope this brief history lesson has helped clear up some confusion for you. I recommend you read about the histories of not only the Martial Arts of Korea, Japan/Okinawa and China but also their political and cultural histories as well. I can't emphasize enough the importance of this in your education if your truely want to understand the martial arts...and have the ability to filter out the B.S.