When referencing "CD-R/RW" discs, it means either one can be used - CD-R or CD-RW. CD-R/RW is not one specific disc format, and it should make no difference. You will never find a disc labeled "CD-R/RW" as such a disc does not exist. A blank disc is either Recordable (R - burn once) or Re-Writable (RW - multi-use). I've been buying blank discs for nearly 20 years, so I'm very familiar with the differences.
You'll notice the page you link to shows "CD-R" and "CD-RW" with nothing for the nonexistent "CD-R/RW" because it simply does not exist. When you see a reference to "CD-R/RW" by a company, it simply means whichever media you need to use won't be impacted by the way the disc is finalized, either CD-R spec or CD-RW. It's simply saying the product can use/read either specification.
The reason CD players can't play a CD-RW is because of the way an RW disc is finalized, allowing the data to be erased, unlike a CD-R. Burning software knows when an RW is used, and finalizes the disc a different way than an R disc is done.
Thank you for trying to help figure this out, though. I do appreciate it.