In "Hills Like White Elephants," the American is accompanied by the girl; the waitress is the woman. What can we infer about the age...

For my
part, I don't necessarily see the use of language such as "girl" or "woman"
to indicate anything unusual about the age difference in the couple.  I think that there
probably is an age difference, but nothing that is extremely different from the norm.  Given how
concerned Hemingway is with "the moment" and the emotional dynamic within it, I think
that the invocation of a significant age difference might take away from this recreation and how
the reader perceives it.  Yet, this does not mean that the difference in terms of language
between "woman" and "girl" lacks significance.  In my mind, Hemingway uses
"the girl" to describe Jig because, to a great extent, she feels like a child placed
in an impossible situation.  Hemingway constructs her character to be posited in a predicament
where there are no easy answers, her helplessness coming across like a child in this situation. 
She doesn't know what is going to happen to the child within her, to the relationship she has
with the American, as well as what will happen in her own life and how this perspective on the
world will change.  She struggles with the notion of going back to the way things were and then
what the uncertain future will be.  She has to reconcile all of this with how she feels about
the American and what that vision of the future will hold.  I think that all of these
uncertainties makes her fundamentally different from all else, and while she has freedom and
might be a woman from a chronological point of view, it is evident she feels like a
"girl," a child searching for totality and absolutes and finding nothing of the sort. 
The waitress is a woman because of the lack of complexity in her life, as she takes the couple's
orders and brings them back beer.  There is a certainty there that removes the wonderment and
confusion of childhood, and reason enough for her to be a "woman."  In doing so,
Hemingway brings out a painful reality regarding freedom and consciousness.  Individuals
possessing freedom, rationality, and a capacity to make their own decisions from a chronological
point of view can be reduced to a sense of the helpless, enabling function to be smothered by
surmise, rendering them to the position of a child in the modern setting.