To add a little clarification. It IS possible to have both and OOW and OOD at the same time. In days past when ships went to anchor for extended periods of time, there would be an OOW with OVERALL responsibility for the ship, and an OOD conducting the "duty-watch" daily administration and routine for the ship. It happens very infrequently now, as the OOW generally performs both roles, it was also more common in a larger ship, such as a cruiser (when we had them) or in the AOR (tanker).
Any seagoing officer can (will be expected to) achieve the OOD qualification; in the Reg force the engineer officers and supply officers must get this qualification in addition to their own. For MARS officers, Reg and Reserve, the OOD must be achieved prior to the BWK (if you look at a BWK certificate it says "...is qualified to stand watch in harbour and at sea"). In the NAVRES, the only seagoing officers are MARS.
NCMs can be OOD qualified, but must be CPO2 or above, and then may only be OOD in Esquimalt or Halifax - this is only done in major warships (destroyers, frigates, tanker, etc.); in foreign ports it is always a commissioned officer. In Esquimalt and Halifax for minor warships (the MCDVs), there is a position called "Senior Watchkeeper" (SWK) that performs functions very similar to OOD, this is a PO2 to LCdr position (although in exceptional circumstances a MS can do it); the roles are so close it makes on wonder why the distinction except that an OOD has more legal powers than a SWK.