A stepper motor has the advantage of precision. You can specify exactly how much it should move and, by setting the interval between steps, exactly how fast (or slow) it moves regardless of load (assuming, of course that it is sufficiently powerful).
If the stepper motor is turning a screw that causes the syringe plunger to move then you are likely to have a very small movement per step, For example an M6 screw has a pitch of 1mm and with a stepper motor that has 200 turns per rev each step would advance the screw by 0.005mm. And with (say) 4 x microstepping that would reduce to 0.00125mm per microstep.