Yes that's right. CD-RW's will only play in your computer, some dvd players, however some of the very newest cd players can apparently play some. The problem with cd-rw's is they have a very low reflective ability. Too low for the average cd player to detect & read. So yes, CD-RW's is the problem you're having.
CD-R's are cheaper anyways.
(BTW CD-RW's are made differently & use different compounds that enable them to be burnt & erased, compared to CD-R's.)