Why do my CDs skip on my new CD player (3 yo), but track perfectly on my old CD player (8 yo)?

Question

All my music CDs play on my old computer, but many skip or don't play at all on my newest computer (3 yo). Also, when I burn music CDs (using CD-RWs), they don't play on the 15 yo Sony stereo in my livingroom, or my old computer's CD player, but everything will play using my CD/DVD player hooked up to my TV?

Answer 1

Older CD players will not play CD-RWs, they will play only CD-R's.
.

Answer 2

2 words: different brands