I absolutely, sincerely hope that I do not offend anyone with my reply, but I am going to answer this question with the way that I was taught to view the subject of Taekwondo. I don't believe in using the term "style" when it comes to describing ANY variation of Martial Art training, and I believe the term is a misrepresentation of what we do, and it definitely should not be applied to Taekwondo. The term "style" is more accurately used when denoting the performance of an individual, how they fight, or their personality as it shows through in their end product. This is something you can mimic, but is not something that you can teach as a separate, unique art form.

For me (and I'm just rambling about my own perspective here), the term Taekwondo was chosen in the Mid 1950s during an effort to unify, and bring together ALL of Korea's native Martial Art, along with modern developments and discoveries, and present it under one title. During that time period, a number of leading Taekwondo Masters founded their own family of schools, each of which had various influences from Chinese and Japanese Martial Art, and each of whom placed a slightly different emphasis on what they felt was important in the development of this unified system of Taekwondo.

Thus, each family was noted as being a different "Kwan," each under their own founder. The Chung Do Kwan was the first to be officially established and given permission to operate as a Korean Martial Art Dojang by the Japanese government in 1944, near the end of WWII. After the war, many of the Black Belts of the Chung Do Kwan opened their own Dojang, but did not remain affiliated with the Chung Do Kwan, thus creating their own Kwans.

General Choi Hong Hi was. like many at that time, trained in some native Korean Martial Art, and Japanese Shotokan Karate. He became involved with the Chung Do Kwan and received an Honorary 4th Dan from the CDK (which was later revoked). General Choi had his own vision of what Taekwondo should be, and used his military position and influence to teach Taekwondo to the ROK Army.

General Choi's family of schools was called the "Oh Do Kwan" which means "School of My Way." Because General Choi created a set of Hyung or tul based on the Shotokan Karate Kata he had learned, by placing Taekwondo moves into the redesigned diagrams, he became known for establishing this set of Taekwondo patterns which he included in his book on the subject of Taekwondo. Since General Choi's penname was "Chang Hon" (meaning "Blue Cottage") his set of forms became known as the "Chang Hon Forms" (also spelled Chang Hun or by modern Romanization: "Chang Heon").

So, while every teacher of Taekwondo is going to bring something new to the interpretation, and presentation of Taekwondo, the core elements that make Taekwondo what it is should never change. Taekwondo is Taekwondo, and you either learn it correctly, and teach it correctly, or you shouldn't call it "Taekwondo" (I don't mean you, personally, but people in general  ). There are some who include tournament training, and others who don't do tournaments at all, but neither of those choices should affect the core curriculum. However, when someone's training is out of balance, and too much focused on sports, while eliminating the philosophy, culture, language, realistic self defense skills, then this is not a different "style" of Taekwondo, it is poor Taekwondo..... or not Taekwondo at all - - just sport kicking!

After WWII, a multitude of Kwans popped up (at least 18 or so). Things were becoming so out of control, and there was no centrally established curriculum for what could legitimately be called Korean Martial Art or "Taekwondo." The leaders of the main original Kwans were attempting to unify under one name, and the Korean Government supported the effort by officially recognizing only 9 Kwans.

“The Korea Taekwondo Association attempted to eliminate the old concept of the Kwan in order to unify Taekwondo. Although there were objections to the elimination of the Kwan system, the Korea Taekwondo Association earnestly began seriously working towards that goal in beginning in 1974. On May 20, 1976, the Korea Taekwondo Association eliminated the names of the Kwans and replaced them with numbers. The following are the Kwan name and their number:

Kwan #1: Song Moo Kwan
Kwan #2: Han Moo Kwan
Kwan #3: Chang Moo Kwan
Kwan #4: Moo Duk Kwan
Kwan #5: Oh Do Kwan
Kwan #6: Kang Duk Won
Kwan #7: Jung Do Kwan
Kwan #8: Ji Do Kwan
Kwan #9: Chung Do Kwan”

The above quote is from the following website:

http://www.martialartsresource.com/anonftp/pub/the_dojang/digests/history.html

Another informative article of in-depth research can be found here

http://www.scottshaw.com/taekwondohistory/

Although the term “style” has been used in modern times to describe various teaching methods, and differing schools of thought among prominent Martial Art Instructors, it was the intent of the unification of Korean Martial Art Kwans to eliminate this concept and combine all variations of instruction into one National Art called Taekwondo. Thus, it is somewhat contradictory, and counterproductive to now try to identify different “styles” of Taekwondo.

Most who have studied Taekwondo history have read a variety of explanations which tend to change according to who is telling the story, and what their agenda is.  Therefore, I do not hold my version, or any of the links quoted here as absolute fact, but perhaps helpful insights to gain a better perspective on what went on during the "Kwan era" and since that time.

Respectfully,
Chief Master D.J. Eisenhart

Very informative post CM Eisenhart!

Most people are unaware that Tae kwon do encompasses many different styles or systems

The majority of Tae kwon do styles are designated by their governing body or organization withing the various countries.

The two most internationally known types of course is the ITF-style, which is governed by the International Tae kwon do Federation or the Kukkiwon style, which is overseen by the World Taekwondo Federation.

The differences among the TKD styles can be seen in their forms and in their sparring. The American Taekwondo Association (ATA) is a major Taekwondo organization in the United States similar to the ITF. Haeng Ung Lee founded the ATA in 1969. Lee developed his own forms he called "Songahm", and hence the name Songahm Taekwondo.

There is also the Jhoon Rhee system of Tae Kwon Do which was established in 1962 by Grandmaster Jhoon Rhee the "Father of American Tae Kwon Do" which also has its own set of forms/patterns

There are many Taekwondo organizations throughout the world, but the ITF, WTF, and ATA have the most members.

I agree with the rest of your very well posted comments. I would only add that the Kwan leaders did not sign on to the agreement till 1978.

Sorry I stand corrected.  I worded that wrong. 

 I try not to say WTF style but rather Kukkiwon style when I explain the sport of TKD.

I suppose in this case I should have said WTF style which is overseen by the Kukkiwon ... in any case I am not affiliated with either.