Welcome to APUG.
This is going to sound familiar to those who read my posts on the subject.....
"Pushing" refers only to the development. It is a label that is often associated with under-exposure, because it is a development technique that can partially improve the results from under-exposed film, but it does not actually refer to the exposure itself.
And be careful bringing your experience with exposing digital into the film world. If you are shooting transparency film, where over-exposure is much more damaging than under-exposure, the "protect the highlights" approach used with digital (slightly reduced exposure) is an equally valid approach.
However with negative film, slight to moderate over-exposure is often the best approach, because the results can be made to look better and more saturated just by printing darker, and because an under-exposed negative may mean that the shadows are rendered without detail.
[Hijack Warning]
Matt,
We usually agree on most everything, but I'm going to argue semantics here with you a little if you'll indulge me
As a Zone System user and advocate, I often use extended development to get more overall contrast on a negative from a relatively flat scene. This, in the ZS nomenclature, is called "expansion," or "expanded development." The opposite of this (reducing development to reduce contrast) is "contraction," or "contracted development." In both cases the film is (or should be) exposed "correctly," that is, to render the shadow details the photographer wants.
"Pushing" film is traditionally used when the one encounters an extreme low-light situation and has to compromise by sacrificing desired shadow detail for a printable negative by intentionally (albeit reluctantly) underexposing the film, then compensating by finding an extended development time that at least gets the highlight values to where they should be in order to print well. Shadows are usually black and detailless. Extending this, some like the look of "pushing" and do it intentionally even when not absolutely necessary, to obtain the goal of featureless shadows and extra contrast. I'll call both of these "pushing."
However, for exposing fully and extending development time to increase overall negative contrast, I'll stick with "expansion."
Transparency film is another beast - and exposures and any development adjustments need to be based on highlights, as you say. "Pushing" here, again however, is compensating for underexposure by adjusting development time. Therefore, the (intentional or unintentional) underexposure of the film is a crucial component of the procedure.
I guess that's the crux of what I'm saying here: "Pushing" is simply compensating for underexposure by adjusting development time. Adjusting development time to control overall negative density range when not underexposing is either "expansion" or "contraction." I find this terminology to be much clearer.
Best,
Doremus