You'll need to tap into far wiser heads than mine, but the shape of your figs sure doesn't look anything like my BTs. I don't know anything about caprifigs, but mine don't ever look like that on the inside, either--even when I get a bunch late in the year that don't have time to ripen, and just dry out on the tree. I'm guessing it's not a BT, but it's just a guess.