Yes, Kwan is a school, or style of TKD. In 1945 there were 5 kwans, and after the Korean war there were 7 that tried to organize to what is known as TKD.
The first organization was called the Korean Tae Soo Do Association, in which all the kwans joined, except Hwang Kee and the Moo Duk Kwan, which split in half over it.
One year, Maj. Gen. Choi was elected as president of the Korea Tae Soo Do Association (was in the position for 1 year) and he got everyone to agree to use the term Tae Kwon Do, so the name was changed. They didn't agree however to adopt the forms he created (Chang-hon) so he left and created his own organization called the International Taekwon-do Federation. After that, the Korean TKD Association changed their name to the World TaeKwonDo Federation, and created a new set of forms in '68 called Palgue and the yudanja forms. In '72, they changed the gup/kyu forms from palgue to Taegeuk forms but kept the yudanja forms.
The Kukkiwon was built and created to oversee all dan promotions, and the WTF just became an international sports organization that coordinates all international TKD compititions.
Hope this helps,