Some threaded rod cutters can look different to others, but they all have the same basic components: base, handle and dies.
The parts housing the dies and connecting the base and handle are subject to manufacturer’s design preferences. But they all work in the same way: by lowering the handle to the base, whilst the dies perform the cut.
On all threaded rod cutter models, one die is fixed to the base and cannot move, whilst the other die moves with the handle. The mechanism by which this occurs is the only difference between models.
However, the dies always perform the cut in the same way. The mobile die is parallel to the fixed one and passes straight down (rather than at an angle or a rolling cut).