No, the whole distinction of black is dark skin colour, which is a proxy for skin melanin, which is (far as I'm aware) the primary factor determining vitamin D production from sun exposure (which is not directly useful in the body, but is the form that is often measured).
Also, because of the effect on vitamin D production from sun exposure, there is some evidence that other aspects of how vitamin D is handled by the body are different for people with darker skin, maybe because their ancestors got more than enough of it.
This isn't even about social categories “Black” and “White”, it is literally about the direct correlates of skin colour.