No, they're not all the same.
There are two reasons for the "no disk" readout..
A: The files are in a format the player does not recognize.
Mp3 or any other compressed format is not recognized by older CD players.
They will only play tracks in wav format.
B: A lot of CD players do not recognize CD-RW (re=writable) disks.
Re-writable disks are mainly intended for computer use.
CD-R disks can be used in any CD player, computer or DVD player if the music is burned in wav format.
Wav format is the same as that used on store bought CDs.
The disadvantages are - CD-Rs are permanent - they can't be erased and re-used.
There is a limit of about 18 - 20 tracks per disk.
Erase the disk and burn a couple of tracks in wav format to it.
Probably the quickest way is to rip them again from the original disk direct to wav.
Burn them to the CD-RW and try it in the player again.
If you get the "no disk" result again you need to use CD-R type disks.
They have the same 700 Mb / 80 minute capacity.
Now you need to find out the file format/s it will play.
Whether a player will accept mp3s will depend on it's age and price range.
Up till about 8 - 10 years ago only wav format files could be played.
Mp3 files are much smaller than wav files and up to about 150 will fit on the 700 Mb disk.
CD-Rs are very cheap and this may cost you a disk but it's the only way to find out.
Burn your original format tracks to a CD-R then try it in the player.
If the "no disk" result shows again you have the answer - wrong format.
The player will only play disks which are CD-Rs burned in wav format.
In this case rip your original CD to the drive in wav format then burn it as an audio CD or if the tracks you've already ripped are in mp3 format simply select audio CD as the burning option and the conversion to wav will be automatic.
Converting to wav from mp3 will not result in as high a quality as wav to wav.
To comment on a statement by the Kool Aid Guy who says his Hi Fi won't play copied CDs.
Again this gets back to the age of the player. One system might play mp3 format and the other doesn't.
It has nothing to do as to whether it's a burned disk or not.
ALL players will play disks burned in wav format.
I've been compiling, burning and distributing CD-R disks burned in wav format throughout Australia for over 15 years and guess what? Not one failure!
The only "secret" to burning a successful CD-R in wav format is to use a maximum burn speed of 24x to reduce the chance of errors during the burn process. Even less is better.
The difference in time it takes to burn is minimal.
Sorry if I've confused you but I couldn't explain it in a couple of simple sentences.
The last time I gave an explanation as detailed as this it was deleted by the site filter as chat so you may or may not get this.