It's by definition a different style, having different patterns, and a different art, not employing shared techniques ( some are, some not).
Make up your mind. First you said they're "not the same art" and now you're saying they're different styles. Different styles and different arts are not synonymous terms.
What they are, is different styles within the same art. Styles with far more shared traits than different.
Tell me the commonalites then, besides both using their feet (in WTFs case rarely punching).
Again, there is no such thing as WTF-style. Perhaps if you ask a question that's not based on incorrect information and false assumptions, I can give you a better answer.
The dobok - not the same.
I wear a different dobak than others in our dojang. Does that mean I'm not practicing the same art?
If I wear my black dobak, am I practicing a different art than when I wear my black pants and white-with-black-diamonds dobak, is that another art too?
Damn, I had no idea I knew so many different arts!
Turning kick/ roundhouse in WTF, is NOT a Mawashi geri as in ITF and it's precedors.
The WTF, not being a style, doesn't define any techniques.
The KKW, on the other hand, does indeed have roudhouse kicks that are done quite precisely the same way as those done in the ITF.
If you think any of these systems of taekwondo only teach one stance, then perhaps I can begin to understand why you seem to have such a poor understanding of them.
Stances may have different names in different schools, but I do not believe you can show me any stance taught in the ITF that is not also taught in other systems of TJD.
Punches are virtually non existent, outside of the pomsae.
Really? That's odd. Our students punch a lot. To the head, even. Perhaps you are confused by the difference between the very limited set of techniques allowed in Olympic competition and the much broader set of techniques taught in both KKW and ITF (and other) schools.
Grading is up to 10 dan, while ITF is up to 9
As with so much else in your posts, you are confused.
The WTF, being nothing other than a governing body for a sport, does not issue rank, define curriculum, or perform gradings.
The KKW grades up to 9. There have been a (very) few HONORARY (and mostly posthumous) 10th Dans awarded.
The Moo Duk Kwan grades to 9.
I don't know about all the various orgs (there are far too many), but other than Rhee TKD, I can't think of any offhand that grade to 10th Dan. And in Rhee TKD, I think GM Rhee is the only 10th Dan, so it's more an indication of who the founder is than a graded rank.
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WTF does not recognize an ITF black belt, as a black belt of Taekwondo.
Etc.
No, the WTF did not allow ITF black belts to compete in WTF-sanctioned competitions, though this is no longer true and ITF Dan ranks are now allowed to compete in WTF-sanctioned events.
There has never been any claim that the ITF black belt is not a TKD Dan rank.
Quite the contrary. The KKW has long had a policy of offering crossover rank to dan holders from other systems of TKD. That would seem to indicate an explicit acknowledgment that these other systems ARE, in fact, TKD.