The True Master Sword is the Master Sword at its full potential.
It’s more or less the same, but it can charge up Skyward Strikes faster and they deal the same amount of damage as regular sword swings.
Also, when fighting Bokoblin enemies, regular sword swings will generally bypass their guard. Furthermore, the spin attack will always hurt Bokoblin and Lizalfos foes, regardless of how they guard.
Where to Find
After visiting the Temple of Hylia, the Master Sword will automatically upgrade to its true version.