The white oak is named for its whitish bark and grey twigs

Yes, it is about coloring/species appearance. In CA. we have Black Oaks.
Same concept, blackish bark and dark wood.

If you place white oak flooring alongside red oak flooring, you can better see the difference.

The white oak’s wood is lighter in hue though not really white. Red oak has of course a reddish hue and is less expensive and more commonly used because it has greater color variation than the wood of the white oak.