THought I would clear something up.
Soul Edge was the original arcade release.
Soul Blade was the Playstation port that had significant enough changes to warant a new name, including 5 hidden characters; Sigfried! (Nightmare Prototype), Sophitia! (No Armour), Sophitia!! (Swimsuit), Soul Edge (The Boss) and Han Myong (Seung Mi-na's Father). Although all of these characters fought like preexisting charactrers (Soul Edge is Cervantes and Han Myong is Hwang).
Soul Calibur was not a revamped version of the original but a sequel. It contained a many new characters and a storyline that followed on after the end of Soul Blade. Cervantes is no longer the host of Sooul Edge but Sigfried is becoming the Azure Knight (Nightmare).
Soul Calibur 2 is the third game in the series but isn't much more than a better version of Soul Calibur. Kind of like Super Street FIghter 2: The New challengers was to SF2. THe Story hadn't progressed at all but there was a line up change, including the removal of Hwang (god knows why), although they did add Assassin as a bonus character who played identically. Rock was also removed and replaced with berserker. The three releases (Xbox, PS2 and Game Cube) all contained a different bonus character. Link for Nintendo, Heihachi for Sony and due to the inclusion of the character Necrid, who was created by the creator of Spawn, SPawn appeared in the Xbox version.
Soul Calibur 3 continues on from the end of the Soul Calibur 1/2 story. Siggy is free from the blade and Nightmare is his own person (so to speak). New characters that push the story forward have been added and both Rock and Hwang have been returned. Necrid is gone because he was a nonsense character, and all the characters have been rebalanced to make a much more even playing field. Kilik's pole is shorter, Ivy has had her move list changed, Sophitia is less of an unstoppable butcher in skilled hands, Talim seems to be doing less damage. Astaroth still sucks and Hwang stills rules.
Thats about it until Soul Calibur 4 is released.