Digital fluid pumps having first and second electromagnetic actuators formed in part by a piston to alternately drive the piston in opposite directions for pumping purposes. The piston motion is intentionally limited so that the electromagnetic actuators may operate with a high flux density to provide an output pressure higher than that obtained with conventional solenoid actuated pumps. The electromagnetic actuator coils are electrically pulsed for each pumping cycle as required to maintain the desired fluid flow and output pressure, with the piston being magnetically latchable at one or both extreme positions between pulses. Alternate embodiments and control methods and systems are disclosed.