I really wouldn't get hung up on the names of the arts. In the west, TKD is a sport, but in Korea I feel it is more of a word for martial art. There were plenty of arts co-existing for centuries, and as of late, you will hear claims that TKD has always existed, but the word TKD is relativly new. Think of the perfectly valid art of Hwrang Do. I've read the Hwrang guys were all weapons specialists, given their profession, and the whole empy handed thing was a non issue for them; yet, there are people studying empty handed Hwrang do... or is it just another way of saying TKD? In that context I would say yes, but your average TKD school in the west is not teaching what you might learn in Korea. Consider that each name you throw at us, is a flavor of TKD, with a whole new set of rules and customs.
Sean