Great thread, CT and all you followup posters!

I think this is the first time I've seen the issue posed in quite this way, which brings up some fairly difficult issue involving the idea of what 'identity' means in the martial arts.
Based on what I've been able to learn about its history—and most of you folks I think have a pretty good idea of where I'm coming from on this point, based on your participation in previous discussions/arguments/shouting matches/riots on the topic—I think it's fair to say that TKD and TSD are the Korean flowering of karate. They share many of the same individual techniques. Many of the hyungs are taken over unchanged from Shotokan (the Kichos are the Taikyoku katas, the Pyang-Ahns are the wonderful, ever-green Pinan/Heian forms, and in schools Koreanized versions of classic kata such as Rohai and Empi are on the syllabus) or else are in effect mixmastered and recombined Shotokan forms (the Palgwes in particular). A lot of the training methods—kihon line drills and so on—are very similar to karate methods.... and so on.
But as many of you have pointed out, there are many differences as well: a karate performance of one of the Pinan kata is almost certainly going to look very different from a TKD/TSD performance of the corresponding Pyang-Ahn form. The mechanics of the kicks are quite different, and their role in the curriculum. There are small differences in the way the hands move in blocking and so on (Stuart Anslow's book has a nice chapter on technical differences beween ITF TKD and Shotokan).
Here's the way I would try to answer the question, if it were practical. Take two groups of very well-trained karateka and TKDists, respectively, with members of both groups having received many years of realistically pressure-tested training in close-quarter street combat. Put them in situations where two members, one from each group, are paired, and in which each of them respectively is confronted by an assailant using the same violent initiations in each case, the same sequences of violent actions, at very close quarters (where most street altercations begin). Here's my question:
will a well-informed observer be able to tell which of the two defenders is the karateka and which the TKDist? In any give case? In the majority of cases? In the great majority of cases? We're talking unchoreographed, totally brutal-realistic street defense here, remember...
My feeling is, the less able that observer is to do better than a random guess, the less distinction there really is between the arts, taken out of the school/demo context. The more they overlap in content, and the more the difference between them are strictly stylistic and only dojo/dojang-visible. And the flip side: the more it's true that successful observers are successful in identifying which of the two is a practitioner of which art just by watching each of the pair fight an attacker using the same attack moves on them respectively , the more the difference between the arts is substantive, not cosmetic.
Do any of you-all have any thoughts on this? I
suspect that the numbers would be no better than chance, but that's obviously nothing more than a gut-reation-based guess...