Ocular implant insertion apparatus configured for screw-type and push-type operation and associated methods. Such insertion apparatus includes a main body defining a longitudinal axis and a plunger, movable relative to the main body, including a rod portion and an operational portion rotatably mounted on the rod portion. One of the main body and the plunger operational portion includes a helical slot and at least one longitudinally extending clearance groove that intersects the helical slot and the other of the main body and the operational portion includes at least one protrusion that is sized and shaped to fit within the helical slot and within the at least one longitudinally extending clearance groove.