Hi Linna,
I have seen a few albeit fairly rare instances of seamen having duplicate Dis.A numbers. Usually caused by a seaman leaving the service and then rejoining again and being given a new number while his old number was still current (poor record keeping). When this situation happened usually one of the number's was cancelled with a note on the card stating why.
Your case is not the same though. On Alexander Stark's record it states: "served as Albert John Hoare with Dis.A number R40601".
Sadly, many of those cards in the Fourth Register of Seamen do not survive so the only way to track someone would be via Crew Agreements.
Both seamen's cards show engaged on CAIRNVALONA 1/1/1934 so focus on that voyage.
Crew Agreements are not available online. For CAIRNVALONA, 140718 in 1934 see this site about ordering same.
https://www.mun.ca/mha/about/orderagreements.php You can contact them first to check if either named seaman is shown on the agreement. As I said previously the official logbook would probably offer up more information if it was available.
To answer your other question about punishments - there were fines of course and the master could give a poor discharge (DR) to any seamen who broke the rules. This could make it difficult for a seaman to get another ship.
I think it fair to say that checking of identity was not a number one priority back then.
Regards
Hugh