Like I said, it is 2 problems: (1) the logical formating of the disk - as rwise2112 stated it must be in Red Book format with only one session which is closed after the write, (2) the laser must be able to read the disk.
Newer CD players have addressed both issues - their logic is compatible for multi-session disks and (quite a while ago) the lasers used where slightly modified in frequency to read the differently colored CDR and CDRW disks. As I said, very old players will have the laser problem - probably more than, say, 7 years or so old.
The manufacturers had to do a 2 pronged attack of the problem to solve CDR/CDRW compatibility, and they did so well. If you want to use a CDRW for audio make sure it is in Red Book format, single closed session with all the files in the proper .CDA format which is a must because CD players, unlike computers, cannot read other music files formats - they don't have the capability. Most newer players will be able to read that disk, but a few out there still won't be able to, even if the disk is correctly made to play in CD players, due to the laser problem. But that issue might be very, very rare nowadays (it wasn't when CDR's & CDRW's first appeared!).
Your mileage may vary...