No - that's not the one. The one I've got has two jaws which separate under spring pressure. One holds the cable outer (under different spring pressure) on the working stroke, but releases it on the return stroke. The other jaw contains the split dies with the holes, which have a sharp leading edge and bite into the insulation, again under spring pressure. They don't need to go through it to the conductor - simply grip it firmly, hence the choice of four sizes, which cover everything I use. It wouldn't be suitable for very large stuff, though - I'd not try it on larger than
2.5mm.The big difference is that it bites into the insulation over 360 degrees - or near enough - where most rely on just attacking it from two sides.
No brand name, unfortunately, although it's built to last with the wearing parts fixed by screws for easy replacement. If I knew who made it. ;-)
I think it came from Maplin, and was expensive.