In the 70's I bought two B-78's. One was as you described in 6MM, had a cheek-piece and a pistol grip stock, tapered octagon barrel. The most accurate rifle I have ever owned.
The other B-78 was in 45-70 and had a straight stock, no cheek-piece and had a very pronounced C-shaped butt plate, blued narrow steel, that was unpleasant to shoot with but the mildest loads. It had an untapered octagon barrel. Both guns had French Walnut stocks and were beautifully blued.
I do not remember references to the word "Sporter" in connection to them.