I'll muddy the waters by throwing out another definition: Rigid Tapping means simply using a tap rigidly mounted to the spindle. It says nothing about how precisely you can stop. It simply implies (requires!) that the axial motion be precisely coordinated with the rotary motion, to avoid breaking the tool. This can be done with any kind of spindle drive, and a spindle encoder. Without the encoder, or other means of providing precise coordination, you must use a "forgiving", non-rigid, tool holder, like a tension/compression holder, or a tapping head.
Regards,
Ray L.