I love this question. I give the answer from someone who was a member of one. Remember that this answer is based on my own experience and knowledge gained from instructors who taught during the time periods given. It will differ from some of the online sources you may find.
I began Mun Mu Kwan Tae Kwon Do in 1975. I will not go through all the Kwans, but yours, Chun Do Kwan, was the first Kwan and actually created before 1945 while Japan still occupied Korea. The second Kwan, Moo Duk Kwan, and the others were founded shortly after the liberation of Korea in 1945. They were not affiliated with one another directly, but did develop TKD under their own founders. Some of these founders had an emphasis in Shotokan. One had an emphasis in Judo/Jujitsu (this would be the Jidu Kwan). Others had a more Kung Fu feel to them. This was the defining element of the different "styles" of TKD. All of them, however, originally trained with Karate/Shotokan kata. Then the Chang Hon pattern set was developed. Eventually, the Kukkiwon was formed and TKD became political, wanting all TKD to be under one roof with one way of practicing, thus eliminating the individual Kwans. Not all Kwans went along with this. The Mun Mu Kwan refused to adhere to the Kukkiwon and continued to teach the way they did when the school was founded in 1966 (it was very Shotokan-like in appearance).
Since 1972, the Kukkiwon has more and more imposed the idea of competitive sport within its schools. This is the reason today people view TKD as little more than "foot fencing" than the martial art it began as. Remember, TKD was developed for the Korean military, not for sport. It was later marketed as sport to the western world. But, there were two Kwans which were taught to the Korean Air Force and Navy and to the US Army Special Forces during the 1960's and early 1970's: Mun Mu Kwan and Moo Duk Kwan. The original form of both of these had more hand techniques than kicking. Both incorporated Hap Ki Do in their curriculum. There was also weapons training in TKD (Kobudo) which included a rifle with a fixed bayonet.
So, to answer your question from today's perspective: There really is no difference in the different Kwans today as they have lost most of their uniqueness due to being under the Kukkiwon.
To see the real difference, you need to go back prior to the pre-Kukkiwon days. Hope this answer helps