Each weapon type has three variations (+8 Bit weapons from the DLC/updates), each one stronger than the next one. For example, for Link's Sword and Shield you have:
Knight's Sword
White Sword
Magical Sword/8-Bit Sword
The number of stars, which goes from 1 to 5, raises the weapon's attack power, but each weapon tier also is completely superior to the previous one. For example, a zero star White Sword is stronger than a 5 star knight's sword. New weapon tiers only start appearing as random drops after being unlocked. For example, you got the White Sword from a chest in Legend Mode, and the 8-Bit Sword from getting to a certain point in the story, after that, they become random drops, which can vary in skills and stars.
For the Magical Sword (and all other tier 3 weapons aside from the 8-bit Sword), you need to unlock it in Legend Mode. The Master Sword is an exception and doesn't really fit into that system. There are no drops or variations, just that one Master Sword you get in the story (although after unlocking every other weapon from the base game and getting 25000 KOs with it, you'll unseal its skill that will drastically raise its power).