Hiten Style and Wuju Style, in terms of lore, are essentially the same, or have the same origins?

I am saying that because in-game, both are actually very similar. Both are on-hit true damage effects. The difference is that Hiten Style's maximum amount of damage is 75 as it only has a base damage and no scalings. While Wuju Style starts out dealing less base damage than Hiten Style but it starts to deal more damage as Master Yi stacks AD because it actually has a scaling.

This makes me think. What if, in lore, the Wuju Style is actually a similar but diferent fighting style compared to the Hiten Style? Peharps a Wuju sword hits harder than a Hiten blade, but it is harder to learn how to wield it properly. Considering that both are Ionian styles, I would not be surprised if the Wuju and the Hiten style actually have the same origins in some sort of ancient Ionian fighting style involving cold weapons, however they both evolved separately.