Without a double-blind test, it's just conjecture. Audio is notoriously subjective, and existing research shows that 320kbps audio is indistinguishable from lossless.
That's simply impossible, the Spotify client does not change your local files, it simply plays through your OS audio stack. You are noticing the difference in loudness, you can't know if the files you downloaded have been mastered the same way than the ones Apple Music is playing.
I just tried with some of my own music, played the exactly same file as a WAV rendered from my DAW and then a very high bitrate export through the Spotify client as a local file, there's absolutely no difference.
Often it’s also just loudness/dynamic range compression.