In the interest of full disclosure, Minor White continued to use (or at least define) the word zone in the old fashion, and Ansel acknowledged this fact.

The late Minor White, one of the great photographers and teachers of our time, adopted somewhat different terminology from my own:  “previsualization,” for example, which I have always considered a redundancy, and “zone” applied to the subject, negative-density, and print values (I limit zone to the exposure scale and use “value” for the other elements).  Personal semantics are of little importance; I would not expect anyone to change his conceptual terminology to match mine.
— Ansel Adams, Polaroid Land Photography (1978, 213)

But in actual practice, White usually used the word to refer to exposure values, and he seemed to acknowledge that Ansel’s use of the word was more consistent:

In this book a few key word definitions seem to be at odds with Adams’s terminology.  The prime example is zone.  In his Pocket Exposure Record . . . Adams has reduced the scope of the word sharply.  Such curtailment is in keeping with his interest in accurate craftmanship.
— Minor White et al., The New Zone System Manual (1976, 9)

More to the point, White’s instructions for making a zone ruler consisted of assembling a series of prints exposed according to zones as exposure values; the print values were not arbitrary divisions of a grayscale.  So, whatever you call them, zones as exposure values still come first.  This is the key to a general understanding of the zone system, espeically as applied to other media.