Regards a eager diablo fan
In truth Tyrael's sword is named El'druin, the Sowrd of Justce (though from the item database It seems it can also be called Skycutter).
As for Azureblade:
Azureblade is the type of sword wielded by Tyrael and Izual.
Tyrael's sword is named El'Druin, and is also commonly called Sword of Justice, although it is likely that the name is refering to the type of sword, and thus referring to Azureblade. Izual is wielding Azurewrath.
As Azurewrath is called an 'Angelic Runeblade' by Tyrael, it is speculated that it might be his own as well.
The origins of the Sword is unknown, but the Azureblade has been used by Tyrael for a long time, and was his weapon of choice when fighting the Dark Wanderer inside the Tomb of Tal Rasha, next to the Binding Stone.
The Azureblade El'Druin is also the sword Tyrael used in conjunction with some sort of spell to destroy the corrupted Worldstone.
So while the syntax is not the best we can infer that Azureblade is a type of angelic runeswords and Tyrael's is named El'druin. Izual wielded Azurewrath.
Meh... took too long to post a reply I guess...