This is another of those fascinating subjects that crops up within the GMB from time to time.
My own limited experience has shown that there has been much variation in what is presented in "regular" literature. For example the following gives a comparison of numbers of types of Bowl, Stem, Knop and Foot illustrated or described in three not-quite-random selections from my (small) collection of books, with the Great Glass website also included:
Glass Through The Ages - E. Barrington Haynes - 1949 (revised 1959)
Bowl ... 28, Stem ... 23 (includes Knop), Foot ... 12
Eighteenth Century English Drinking Glasses, An Illustrated Guide - L. M. Bickerton - 1971 (revised 1986)
Bowl ... 14, Stem ... 16 (includes Knop), Foot ... 6
An Illustrated Dictionary of Glass - Harold Newman - 1977
Bowl ... 22, Stem ... 30, Knop ... 24, Foot ... 19
Great Glass website - Philip and Ann Petrides - 1999 to present
Bowl ... 15, Stem ... 10, Knop ... 12, Foot ... 6
From just those few references it is clear that there is much variation in numbers covered but it is not easy to understand why some forms were, or were not, included. One thing that has puzzled me (but which I have never tried to follow up) is whether or not the difference in numbers between Haynes and Bickerton gives a true reflection of "English" vs "Other".
However, the Foot illustrations in Great Glass are actually the same as shown in Bickerton's book. Therefore the point that Jay rightly makes about a solid terraced foot is answered by the fact that both Great Glass and Bickerton show only "18th C. English" forms. I have made this comment not to specifically answer Jay's question (which may well have been rhetorical) but to show the sort of problem that can arise when researching information from limited sources.
But who amongst us has a full set of literature from which to draw inspiration? Frank's Glass Study is impressive but, as he says, is incomplete. And I am sure that Adam Aaronson won't mind me saying that, having seen (some of) his collection of books on glass, I realised how lacking my own collection was, and still is.

On the general question of what is it that is being described in text or images, I believe it has always been the case that it is the external form. Where an internal element is of particular interest it has usually been described as an additional aspect - such as the capacity of the bowl of a "toastmaster glass" (also described as a "deceptive bowl") or the shape / size of a "tear bubble" in a stem.