I have a now mostly gray (and brown beard.) My admittedly rough empirical view is that the gray hairs grow more quickly. If I trim the topmost layer, the beard appears browner. I do not think that this is wholly due to the gray hairs being stiffer (thicker?) and therefore stand above the brown hairs.
My simplistic idea is that now that the gray hair root does not have to produce melanin it devotes those nutrients/energy to faster hair growth.
As I have only shaved for 3 months of my life I can not answer your question more fully.
It may be due to a semi transparent layer (sheath or cortex)(in some hairs) that transmits skin colour only after some tapering due to wear.