CD players have error correction built in to fill in gaps in the music (Fault on the disc/dodgy transport), and this can cause the data stream to be corrupted (IE: The error correction does not fill in the gap correctly), and a DAC can only produce what it is fed, so yes, there can be difference's on bad discs or worn drives, but the difference is small.
If you want to hear a CD at its best, rip it to external storage via a computer and save it in Flac format, as a good ripping program will not use the error correction in the CD drive, but will instead read the disc multiple times until it gets the data 100% correct. (And yes, the rip will be equal too or better than the best transport out there, no matter the price)
Spotify is a compressed format that removes musical information from the original recording, whereas a CD does not, however compressed formats can sound slightly softer and more pleasant than the original recording, but it is not as the producer intended.
This is why there are 2 types of Hi-Fi enthusiasts, those that want as much accuracy as possible (If its a bad recording it sounds like a bad recording), and those that what something that sounds nice, there is no right or wrong, just personal preference.
Bill