Yes non-relativistic QM uses Galilean relativity and it embodies
absolute space and universal time as it is entirely like classical physics.
You can make it match to some extended non classical physics of atoms and particles by doing a series of fudge adjustments to the mathematics but there is no obvious reason why the fudges are needed. Without the fudge values the answers are as badly wrong as classical physics predicts.
In Relativistic QM the reason for the fudges and the values becomes obvious as being adjustments demanded by Special Relativity with it's relative space and non universal time. It also makes a number of predictions to do with spins that have no reason for being such in non-relativistic QM. It predicts things like anti-matter because it makes clear that negative energy must be just as valid as positive energy as you have no preferred reference frame. Again you can patch non-relativistic QM to embody these changes but in the meaningless way and concept that simplifications entail. I kept trying to make you look at negative energy which is a real problem in classical physics and it's preferred reference frame (Energy can only be positive).
Relativistic QM can answer almost every problem correctly except one that is close to your heart. It can not correctly describe matter creation and annihilation. You are probably going to ask why? The answer is simple it requires two particles to create or destroy and a reference frame connecting them as we are dealing with waves
https://en.wikipedia.org/wiki/Matter_creationhttps://en.wikipedia.org/wiki/AnnihilationIn the 1930's and 1940's it was thought that matter could neither be created nor destroyed, the phrase is often repeated in error even today. Dirac can be said to have made the first steps to solving this in 1933 but the point is arguable.
The only known theory and reference frame that can solve that problem is a field in QFT.
I am taking a hatchet to history here because there are some sub stories between this stuff but I think that is the level you want.
