No, it's not the same sword from Kill Bill—sorry, Tarantino conspiracy theorists.
But the Japanese sword that Butch chooses to dispatch Maynard still has some symbolic significance. In fact, it's related to the importance of his gold watch, which connects Butch back to a time in his family when men were heroes instead of palookas.
Butch considers a few other weapons before settling on the sword: a baseball bat, a chainsaw, and a hammer. Definitely ordinary objects. But he chooses something extraordinary to begin his redemption: a sword that's part of a culture that had a deeply embedded code of honor. Unlike Butch's, which up until this moment didn't have much of a moral structure at all.
By choosing the katana, Butch aligns himself with the other heroic warriors in his family as he chooses to rescue Marsellus instead of leaving him to a horrible fate. He's getting a look at some greater meaning beyond his own survival. (Source.)