I do taekwon-do (ITF). I understand you do taekwondo (KKW). I don't know what tae kwon do consists of... Essentially, the organisation is what defines it. The organisation is what steers development, defines the focus, sets the sparring rules and format and provides the core curriculum. That is what shapes the art. A little example - if you were to come sparring with us, you would probably get punched in the face a fair few times (in a nice way ). The look of the art is very different too - compare stances and movement in some pattern videos on YouTube (if you don't know what to look for with ITF, I can link you if you pm me).