A CD-RW don't reflect as much light as a CD-R due to the different composition of the reflective layers. The CD-RW layer is designed to be able to be melted so that it can be wiped and re-used and cannot be made as reflective as that of a CD-R which just needs a one-off pit burnt into it.
The sensor in a computer CD/DVD drive is designed to be sensitive enough to detect the lower amount of light reflected by a CD-RW, those in audio systems normally are not.
The sensor in your CD player just can't see CD-RW disks.