I’ve found out some more information while I am waiting for the records, which might help other people, so I thought I would post it. I tried to find out if there was any connection between Royal Navy personnel and the Merchant Navy and realised that there was as they were involved in protecting and defending the merchant ships and sometimes served on the merchant ships also. I thought I had solved the mystery but when I looked at the National Archive catalogue where Billy’s records have been filed, the description was referring to army, specifically Royal Artillery Service, as well as other roles. This confused me even more so I did some more research to see if there was a connection between the Royal Artillery and the merchant navy and found that gunners from the RA served on merchant navy ships to operate the guns they were fitted with to protect them. Here's a few links for anyone interested:
https://en.wikipedia.org/wiki/Britis...f_World_War_II
This was interesting part for me:
Attachment 37960
This is the article that says about the connection with the Royal Artillery and the maritime regiment:
https://ra39-45.co.uk/units/maritime-ra
Interestingly, it says they were issued with 'naval kit', which I am assuming might have been uniform as well.
Attachment 37961
I have read that they needed to keep the gunners' presence on the ships as secret as possible so they were listed as part of the crew.
I can't be sure but I am hoping that this might explain the confusion with my grandfather, as I have since found out from my MOD request, prior to my NA's order, that his record is for the army. I will only solve the mystery when I have the records (i hope!), but this may help someone else.