This is where the Relic quests get so darned confusing. Because, while there is only one Thyrus, only one Curtana, and so forth... there are apparently multiple Stardust Rods. And, though I've been led to believe this isn't the case, I swear I read that the Omnilex was part of the standard Scholar uniform. Gae Bolg is a title for a lance, not one particular lance.
But that's just roleplaying with very finite resources. Just because there's more than one Stardust Rod doesn't mean everyone can have one... and then when people start laying claim to them, bad things happen. Hence why I like the replica/ "Like X but not" theory, for sanity's sake.
OHgod that is terrible confusing. I have only done the Thyrus and Artemis Bow so I had no idea!