Screen recording is nothing more than recording what is seen, which does not accurately represent the actual quality of the streamed media itself.
The stream is the 4 GB version, the screen recording was done at a 60k file bitrate, resulting in 25 GB, which is simply insane. So while the screen-recording file might be great quality, spec-wise, it is unnecessarily bloated, since it won't change the result if you lower the quality until it matches the actual stream bitrate.
So basically, it's the equivalent of recording a Spotify song and exporting it as 96kHz lossless WAV file. Meanwhile Spotify is only providing 192kbps OGG, and I think 256kbps for Premium users, if memory serves right.