And I also caution you to evaluate your paint with all samples of all hard elements together - so any wood, stone, tile, carpet, major textiles like sofas, bedding, etc ALL together at the same time...again, pure white is great for cabinets and trim but something soft and not so bright for the walls will look more pulled together and ‘finished’. Your first inspiration pic where all walls and trim in all one color is not a bright white like Pure White. Your second inspiration pic which shows only trim/wainscot is probably a brighter white like Pure White however then I ask what was the wall color used with it and with what other fixed materials? If you want a complete white on white look like your first pic you will need to go darker than Pure White (IMO and Maria Killams:)

I suggest you check out this LINK to Sherwin-Williams site. Click on a color to see its name and how it looks in a room. Other than High Reflective White, Snowbound is perhaps their lightest "white" though Ibis White and Arcade White are also quite light.

drift of mist is a light grey paint option. it's greige . I painted my walls with this color throughout my house

Thanks everyone. There is not a window in the powder room. Vanity is white, tile floor. I have the Sherwin Williams book of colors so I am working hard to find a good gray color. The granite counter is a blue gray which is why I am looking for a cool gray.