as I understand it... generally it's the size of the inner core of the string and not the winding diameter, which is why a strat for example will most often have the two 'stair steps' at similar placement (cores of the wound strings are roughly similar diameter as the plain strings).
I think I've got a tapered B on my old Chap 5, it's roughly a 'straight slant'. As a sidenote; there's a youtube review of a low cost headless bass, a model that I own and like, where the guy goes on and on with difficulty setting it up after a string change, FINALLY getting to the point: he put standard scale with tapered B strings on his fan fret (35" scale) headless: the taper on both ends, especially at the nut made it impossible to setup.
'User-error' ("what does this screw do?") is very common with used gear, I've been guilty but improving. When buying used bikes to flip, I call it 'the mark of the bonehead', - something has been adjusted or setup weird, now where is it? More common with bikes, but not uncommon on guitars