There is no difference as far as I know between "(Quick Effect)" and "During either player's turn".
"(Quick Effect)" is post Link/VRAINS/Master Rule 4 era AKA the newest way.
Cards that use "During either player's turn" Master Rule 3 and earlier.
"(this is a quick effect)" is used in Master Rule 3 and back as a specification for quick effects that broke the pattern by being quick but only during your turn rather than "during either player's turn". I don't think they have a Master Rule 4 equivalent since "(Quick Effect)" already covers that as well, and it was not a very common specification.
Well I guess long story short... I'll just keep the wording as is then. I am not mentally adequate enough to be worried about wording right now. XD I was looking at the True Draco Continuous Traps to try and assess all this. Can't come up with a conclusive call. Guess it is just a hypothetical wording/ruling Konami could dump on us at any point if they really wanted to.