Let's talk about Red Magic.

[Shurrikhan]

See, I thought Fleche and Contre Sixte swords were made of Ice. But since they don't add to the gauge I imagine you're right and that they're crystals. In my opinion, RDMs developed some unaspected (and thus unaligned) spells for their repertoire. Think of like how Arcanists use Ruin, an unaspected spell. Jolt/Jolt II are likely the same idea, with the express intent to enable dualcast, as a Red Mage's White and Black Magic spells are powerful and have involved casting times.

They both do piercing damage, iirc. Sharp icicles in this game apparently do not. Clearly they must not even be swords, but sword-shaped arrows, bullets, or spears.