I agree that they're related, but I don't think they're identical, and I do think it's interesting watching them drift. I agree entirely with your definition of "white privilege" (and "male privilege", "het privilege", etc). But privilege covers a myriad of things - there's a reason it's "unpacking the invisible knapsack" and not, say, "unpacking the invisible box", where a box often contains one item but a knapsack can be assumed to have a bunch of stuff in it.

In this case, you used the term "white" in reference to the one aspect of safety from persecution, and it's a good usage because it was vivid and immediately intelligible. But even though it's really just a sharpening of a concept in one particular direction it was new enough to me that I found it interesting. I expect I'll be seeing it used that way more often in future.