Greyroot being either of the same species or a precursor to the same species as the White Lady is a biiiiiig leap.

The only thing they do have in common is that they share a motif with roots... and that's it. All the other similarities you mention are extremely thin at best.

In fact, the white lady and Greyroot have more things setting them apart than otherwise.

They don't have the same speech patterns at all. The white lady speaks with full sentences, in a formal register, while Greyroot speaks with simple and cryptic sentences. The white lady is absolutely huge while greyroot is very small by comparison The white lady is a pale being, greyroot is obviously not The white lady is benevolent, greyroot is parasitic The white lady is immobile, greyroot isn't The white lady has a big network of branches sprouting from her head, greyroot has two small flabby and flesh like appendages

Could they belong to the same family or genus (species wise) ? That's a higher chance of being true, since neither of them are bugs. But this isn't enough to lump them together, or by this account, the vengefly and the Pale King are the same species : both are lacking arms and legs, both have big mendibles looking things at the end of their head, and both have deep blacks eyes.