With examples like Cure I personally think your probably looking at a situation similar to what you see a lot in real world Martial Arts. While many aspects of Martial arts are quite different there are a lot of similarities. For example, a lot of the grappling and choking techniques used by Jujitsu are almost identical to similar techniques you see in old Western Martial art Journals. The reason is simple. Mechanically its the most practical and efficient way to achieve the grapple/choke.

With spell casting it could likely be the same thing. Curative magics would be exceptionally valuable. Realistically there is probably only so many ways to efficiently manipulate Aether to create such magics. It wouldn't be surprising that people would develop methods of spellcasting that are similar since mechanically Aether works the same regardless of where you are in the world.

Is the magic that Garlean conscripts use Conjury? Maybe not exactly but I would think it very likely its a close relative.

Here is the thing about White Magic though which makes it stand out. Power. No other form of healing magic which doesn't use things like supportive tech would be able to generate as much Aether for a single spell, at least from a mortal. All that extra power means that White Mages would be able to perform spells and do things that were just literally impossible otherwise. For me this is why White Magic and Black Magic are more tied to the Aetheric Drawing method. Due to all that extra power they can do things that are simply impossible otherwise.