Part of the problem we're having is that we are talking as though there is a simple unitary denotation of 'taekwondo'. But there isn't; my viewpoint is very similar to Errant's, because my lineage, Song Moo Kwan (an almost word-for-word translation of Shotokan) has never strayed very far from its roots (like those of the other Kwans) in Japanese Karate, and the version of TKD that I study and practice is similar in intent, especially in its SD applications, to karate. But there's a whole continuum of styles and objectives within TKD. And that's just the beginning of the problem...
... because you have to define better what you mean when you ask, is X the same as Y? In terms of martial arts, what are we talking about, really? Basic elements, partly; how they're put together, partly; what the strategic 'master plan' is, partly, and so on. I've seen enough of the FMAs, and other KMAs such as Combat Hapkido, to be pretty sure that TKD is not the same as either, because TKD consistently offers different solutions to a given self-defense problem than either of those do. But in a given street confrontation, does TKD (taught with the intent of providing you with robust, effective, realistic techs) dictate that you do something very different from what TSD teaches you? My impression, from the TSD I've seen, is that it doesn't. I suspect Upnorthkyosa and I would want to do very similar things in the face of a given violence-initiating move. Maybe TSD has a different curriculum from my school, but there are probably a lot of TKD schools whose curricula are at least as different. I don't know that there's enough of a difference to make a difference, in the realm of crucial action.
Let's face it, the only thing that isn't different from X is X itself; to me, the important question is, how different are the two things you're asking about. I just don't see that much difference between TSD and TKD, from that point of view...