I think the misunderstanding here is that in naval ships there’s a crowd of people taking over and a crowd being relieved. Invariably there’s a bunch of junior officers under training competing for time on the bridge and depending on their competence the fully qualified OOW may delegate duties from sharpening the pencils and answering the phone up to and including taking the watch including the con, navigation, collision avoidance, station keeping, manoeuvring, zig-zag, etc.
So it is vital for the helmsman/quartermaster to know who is giving the orders from amongst the clutch of officers present. He would be told who has the con. In former days, when the helm was below the bridge somewhere, there was no need to specify the con as all voices from the bridge were obeyed.
The crowd on a merchantman’s bridge is slimmer and hence no need to specify the con.
Just to add some good solid naval BS to the system, I have strong memories of my time as OOW of the (temporary) flagship, a “fast” replenishment tanker. With the admiral and his staff embarked, no other ships in the fleet to worry about - we were racing across the Pacific to catch up with them and get to your Independence Day in 1976, there was more than a crowd on the bridge whenever the admiral decided he didn’t like the movie in the wardroom and wandered up to the bridge.
Picture the scene. The admiral would normal signal the fleet his night intentions ie course, speed, formation, command arrangements, manoeuvres etc. So the admiral and his staff populated the port side of the bridge (in a proper flagship, he’d have his own bridge) and the ship’s captain and staff on starboard. The navigator would point his dividers to our precise position on a chart of the whole Pacific and the admirals staff would discuss this momentous news and compile a signal, released by the admiral, from OTC to all ships under my tactical command - night intentions encoded etc.
That was transmitted by radio to the non-existent fleet and duly received by the ship’s operators on the starboard side. The ship’s signal yeoman would decode the signal and call, "Captain, sir, OOW, message executed with a time to all ships, night intentions etc etc. We would chorus our understandingmand the admiral would depart and a dozen officers could return to the wardroom movie and I as OOW could sneak back into the captain’s chair and quiet bliss return.