I was raised in Texas, so it is all “coke.”
I learned “dead front” all those many years ago. About only time I use the term is when it is missing or loose. Maybe it is a regional thing, because I hear the term here whenever these discussions come up.
Good point. Would you say “panel door” for the outer door/cover?
I’d say, “panel cover door” to be a bit more precise.
IMO we have to strike a balance between what makes sense to our clients, while at the same time what makes sense to the contractor who might be making repairs.
True. In my area, if I referred to a panelboard as a load center the client would have no clue what I am talking about without a photo 
We refer to them as electrical panels and electrical sub-panels and panel covers or panel dead front covers. I am less generic in commercial inspections reports.
I agree, I wouldn’t use the term load center either that’s right up there with Sawzall and Skil saw.
Deadfront is an adjective. It is also one of the most misused and abused terms by home inspectors. Not all panel covers are deadfronts and not all deadfronts are panel covers.
In residential electrical systems the panel covers are almost exclusively deadfront covers, but to call them deadfronts is dead wrong. They can be properly called deadfront panel covers, panel covers, or simply covers, but to call them deadfronts is wrong.
In residential electrical systems there are panel covers that have an integral floating deadfront panel. The panel cover and the deadfront panel are not intended to be separated. When the cover is removed, the deadfront panel is removed with it because they are attached together. In commercial electrical systems, it is common for the deadfront panel and the panel cover to be two separate components.