Princess White (also called "Super White" or "Vermont White") is not a "true" granite, but a quartzite with minor impurities. So, yes, it is the same thing as quartzite, in terms of composition & hardness.

Some sources list it as a granite, which is incorrect, and others make the even worse mistake of listing it as a marble (it may look marble-ish, but Mohs hardness of 7 is waaaay different from the Mohs 3 of marble).