I once asked about this myself, and it does depend on who you ask. Not everyone in customer service has a list of the differences between some parts & assemblies. Sometimes they can go ask someone else who does, though.
I was finally told that the same magazine bodies, same followers, same magazine springs & same magazine butt catch assemblies were shared by the CS9 & ORIGINAL 3913TSW magazines ... but they had different butt plates. That means they have a different part number for the assembled magazines.
On the other hand, the CS45 & ORIGINAL 4513TSW do NOT have the same 6-rd magazine bodies in one critical respect ... which is that the CS45 magazine tube has a secondary set of indentations added to the area of the feed lips (one on each side) to help prevent the displacement of the top round under the increased recoil of the .45 ACP round.
When it was determined that the second set of indentations was necessary to help prevent feeding problems in the hard-kicking little .45, they were added by hand to magazine bodies which had already been produced by a machine shop under contract to S&W. This was only a temporary 'fix', as the production of the magazines was then changed to add the indentations during regular manufacturing.
Sometimes figuring out which parts are used in which guns, or may be used in different guns, can be a challenge. I've had to have the folks back there call and ask someone to consult a production book, or call and ask an engineer, more than once.