That's the higher-level version of the Star Dragon Sword in Suikoden I. You get it when the SDS is sharpened to level 12. It doesn't exist in S2, IIRC.
In Suikoden 1, Viktor gets the Star Dragon Sword. If you upgrade it enough it turns into the King Dragon Sword
Barbarosa's sword is called Dragon King Sword, the "King" and the "Dragon" are switched around. Lol.
I'm pretty sure that's a translation issue.
If I recall correctly, the Zodiac Sword was mistranslated as the Star Dragon Sword. In all probability, its sharpened version was also mistranslated. Thus the odd coincidence in names of the King Dragon Sword and Barbarossa's Dragon King Sword.
Much like the True Holy Rune not being a True Rune.