Sword: You acquire it through normal gameplay and is necessary to continue the story. It's a very basic sword with no remarkable designs, but sturdy and more effective than the wooden stick when it comes to combat (obviously)
Mace: A very powerful weapon, capable of cutting ropes like the "Sword" (don't ask how) and is far more effective in combat, usually not requiring more than 2 hits to defeat any enemy. Acquired on your first run through the game as a hidden weapon.
Light Sword: The only info I have on it is that it's acquired at the same place and same way as the "Mace", but only during a New Game+.
Queen's Sword: Also required to progress with the story, it is the ultimate weapon. It will destroy any Shadow with one hit and can protect you against their darkness.
NOTE: The Queen's Sword was available in Shadow of the Colossus as the very last item you acquire from beating all 16 colossi in Time Attack (Hard) and killed any colossus with one strike. It was added into the game as an Easter Egg from Ico. Although the story for Shadow of the Colossus predates ICO, the latter came out several years before.
Also, these two games are not the only ones that have a weapon called Queen's Sword. Many other games have sword weapons bearing the same name. Most of these came out years before either ICO or Shadow of the Colossus, so it is not originally from either game.
The idea behind ICO's "Queen's Sword" is not completely revealed. Some would assume it is the Shadow Queen's sword (Yorda's mother), however, it is obvious she can not wield such a weapon as it would harm her, if not kill her. Possibly, the Shadow Queen was once a queen of that castle, but was corrupted and taken over by the darkness?
Since she wants to use Yorda's body to renew her own, it's safe to assume she's done it before as boys with horns have been being sacrificed there for a very long time. The spell for renewing her body would come from the "castle" in Shadow of the Colossus, where Wander was reborn as a baby with horns (after being infected by Dormin). The Shadow Queen, not wanting to die, discovered a way to prolong her existance, rendering her virtually immortal.
Although most of that was off topic, atleast now you know something more about the game.