This is the road to madness that ends with trying to discern differences where there are none and spending too much money and storage space on hi-res files you don't need.
Sometimes Apple Music encodes sound a little bit different because of the Mastered for iTunes program, but you'd have to be a dog to notice a difference between the two services on highest quality.
Did you try it?
I was thinking the same but I can't say that the differences are only heard by dogs.
Had a few friends take a listen on good eq and they all could tell that they sound different and which one sounds better.
I don't know if it's every song but most things I listen too have huge differences