Yep. All of it is just emergent shorthand, and none of it makes literal sense. :) If we had some specifically correct terminology, it would likely be quite a mouthful, either including genetic terminology or some mix of geography and time period, but both of those would probably still be insufficient. Race basically doesn't really exist in any clean delineation.

>Weird in its own way. White is a skin tone, Asian is a geographic location.

Asian is also a skin tone: the Middle East is in Asia, but counts as White for the US Census.