Yamato was a demon forged katana that Sparda used to kill demons. I think he got it after sealing his power. Yamato has the power to open the gates of hell. Not sure if in only fortuna or every hell gate. There are two versions of Yamato
DMC1 Yamato (early design)
and DMC3 and DMC4 Yamato
If Vergil makes an appearance in DmC, then Yamato will probably look different.
Now Sparda's sword, the Force Edge, is Sparda's most powerful sword, and it carrys his power after he sealed the hell gates with it. Whoever possesses it can gain his demonic power. There are two versions of it;
It's sealed form (Force edge) and it's true form (Sparda)
Nero's sword Red queen, has no special perpuse, however, it is a unique sword that has a motorcycle engine on it that makes the blade ignite and more stronger.
And then there's Rebellion. It was given to Sparda I think after he sealed his power. It was more of a sword he used for a handicap compared to Yamato, and it made fighting demons I guess more harder. There are 4 versions of Rebellion
DMC3
DMC4
DMC2
And DmC
Out of all these swords, Rebellion is the most sword that has no real special purpose or no special uniqueness. Red queen ignites the blade, Yamato can cut through anything and can open the hell gate, Sparda (Force edge) has all of Sparda's power in it, but Rebellion is just a magic blade.