Likely a slightly warped CD case with a grippy bit in the middle that's undersized.
Which means the discs can rotate and then collide with the case. But key to the scratches is the undersized grippy thing, a good case won't let your discs spin.
Cheap cases have been doing that since I was a kid and I burned my first CDs back in the day. Nothing quite like being the cool kid with a CD burner back in the day.
This wear pattern is formed by spinning while some rough object touches the disk. Are you spinning them a lot in the cases with your fingers - absentmindedly? If not, it's for sure the player.
That looks like damage to the plastic coating, blast from the past, but you could just throw them in a resurfacer if you can find one, every resurface will be less reliable than the one before it though.
May not be worth it, how old are these? My knowledge is maybe out of date, but if it's a dvd-rw opposed to a generic dvd-r, the usable lifespan used to be pretty limited. In theory, manufacturers claim 10-25 years based on their accelerated testing methods, but in actual lifespan, some data hoarders were seeing numbers average as low as 2 years for large collections. No good studies out there I'm aware of though. I used to have all of my media on dvd-rs and almost all of mine were showing read errors after 5 years, even the ones from the good manufacturer, this was back in... 2010ish.