Fidelity is the characteristic of whether the playback matches the input.
There is no subjective component to this and it can be measured with significant precision.
A recording/playback chain with perfect high fidelity will be virtual indistinguishable from the original.
If all music were live and extremely well recorded, I doubt there would be as much division as we have about what sound quality means. But not all music is "live," much of the music we hear is painted by musicians and recording engineers (and, one could argue, then fouled up by the producers). The gold standard then becomes the aural vision in the head of the recording engineer. Sadly, even that gets polluted over time by the mastering and duplicating process.
So as not to ramble, the truth is that the recordings we get to listen to vary widely in their fidelity to either a live event or the aural vision of the artist. For example: the Django Reinhart recordings I love so much have miserable fidelity. So while I'd like to say that sound quality is simply a matter of fidelity, it's not practically the case.
This whole hobby is about people having some set of favorite types of recordings and their typical lack of fidelity, which provide us the opportunity to editorialize by selecting certain reproduction equipment that will be pleasing to our own ears. One can somewhat characterize that gear and the typical characteristics of the music we listen to in terms of their 'sound qualities' such as 'lush' or 'fast' or 'punchy', and these terms would be meaningful mostly in a subjective way.
While I would love to believe sound quality is fairly narrowly and issue of fidelity and can be objectively measured, practically speaking, it's not.
I need to add here that if the people who produced the music would get out of the way of the people who create and record the music, we might be quite a bit closer to being able to deal with sound quality in a more objective manner.
I'll also contend that when we do find a recording with very high fidelity, it is the gear with the highest measures of objective performance that will deliver the most natural listening experience.
Gear with good objective measurement will offer you the best fidelity to the original signal.
Gear that editorializes in accord with your taste will tend to make recordings more pleasing to your ears, but may degrade the intended experience of extremely high fidelity recordings.