They are indeed blacksmith's taps, and the explanation of how they were used is generally correct. I don't remember the episode number, but Roy Underhill ("The Woodwright") visited a blacksmith, who used such a tap to make nuts. He went in from one side until the male thread would go partway in; then he finished from the opposite side, so the nut had a fairly tight fit at its center, with a taper going in from each side. The die he had more or less swaged the threads, rather than cutting like modern dies do. It was a two-piece, with some adjustment. The number of threads per inch was the same for tap & die, but diameter wasn't precise at all. When the smith made a part, the diameter of his raw part was whatever it happened to be; he needed to adjust the die to match. It might take several passes before he got decent threads full length. By that time, the diameter was fairly uniform, but its size was luck-of-the-draw. The tapered tap let him make the nut to match.
Be on the lookout for dies (or diestocks) to match these!
