Almost all the early pace bowlers bowled 'off breaks' at very high speeds which were not very different from the 'slower 'off break' bowlers as far as grip and delivery of the ball at release were concerned.
It would become too nuanced and an exercise in futility if we were to describe the bowlers by the grip alone.
One sees similar debates on what constitutes a 'wrist spinner' and people write of Murali as a wrist spinner. This is again getting into semantics rather than what the bowler is trying to get the ball to do, which is 'break from the off' which is what off break is supposed to do. Just like a leg break is one which breaks from the leg.
The off cutters and leg cutters came later with the finger just moving (cutting) across the seam to give the movement off the wicket in a direction different from which the ball would have moved off the seam if it had not been 'cut'.
In very old texts one finds most references to bowlers as just slow bowler or fast bowler. The difference was probably only in trajectory with the slower bowlers tossing the ball a bit in the air at the time of delivery. That is why so many bowlers we classify as spinners actually opened the attack on so many occasions. The line was hazy and some of the 'spinners' or 'break bowlers, bowled at pretty high pace.