The pressures originate from the pumps (i.e . when testing a casing shoe) and the formation (i.e . when the well kicks) is hydraulic imposed hydrostatic

The pressures that originate from the pumps (i.e., when testing a casing shoe) and the formation (i.e., when the well kicks) are hydraulic pressures. Hydraulic pressure refers to the pressure exerted by a fluid in motion, such as the fluid being pumped into the well. Imposed pressure refers to external forces applied to a system, while hydrostatic pressure refers to the pressure exerted by a fluid at equilibrium due to the force of gravity. In this context, the correct term is hydraulic pressure.