It may be worth pointing out that the series contains other weapons that are distinct from, but in some ways similar to, the Master Sword. The Four Sword (aka Picori Sword), for example, is a distinct sword, but it can repel and banish evil, and has even been used to seal Ganon. It's even appeared in the GBA remake of Link to the Past, being clearly distinct from the Master Sword, as you must reconstruct it after completing the main storyline.
As such, as a bit of a frame challenge, there is no need in principle for the "Magical Sword" to be the same as "The Master Sword", as there is no requirement for there to be a unique sword capable of dealing with evil/Ganon.
Also recall that in the original LoZ the sword was irrelevant to the adventure*, as the only essential piece of gear to the final boss fight was the Silver Arrows; you could be using the wooden sword and still defeat him as long as you had the arrows. All the white or magic swords did was increase your damage. So, indeed, we can frame challenge even further, as the Magic(al) Sword does not even require any abilities regarding evil that we see in the Master Sword or Four Sword.
*Indeed, this can also be said of Breath of the Wild, as again the only weapon strictly required for Ganon's defeat is the Bow of Light, which is provided by the plot. The Master Sword is strictly optional, even outside of speed runs.