Let me try something else here, which may (or may not) shed some more light on the subject.
Seems to me there are basically 3 main "flavors" of waveforms:
(Attachment Link)
(obviously the bottom-left quadrant, alternating but not varying, is nonexistent)
There don't seem to be any accepted terms for these categories, except that alternating/varying is, in its pure form, AC, and not-alternating/not-varying is, again in its pure form, DC.
But of course there are variants of each of these "flavors" which can be disputed.
Maybe we need some more terms (or categories) for this?
Perhaps for some well-known examples (half- or full-wave rectified sine wave, positive- or negative-going square-wave pulses, etc.)?
Or do we only need, as some have suggested, to be precise in our description of any given waveform?
DC is not just a straight line at a fixed level for many people; DC isn't an acronym owned by anyone, and for millions of people who are in technical engineering vocations and are indeed engineers, DC means some sort of connection with a pair of wires where one is always "plus" with respect to the other one, and if the signal doesn't visibly change level much on the multimeter, then that's maybe a bonus but not always.
Even for design engineers who may well use equipment to observe signals in extreme detail, DC can still include a signal that varies over a period that realistically might not even be "long".
Part of successful comprehension for engineers relies on recognizing context and recognizing when they need to give or seek additional information and knowing how to do that.
Part of successfully conveying information comes from recognizing your audience.
And, if you recognize that your audience needs particular levels of accuracy, then there's still really no point in trying to be accurate with written words alone, because if the audience is deeply technical, they will simply expect you to have provided things like diagrams, or maybe even photos or maths formulae, or additional material such as specifications or schematics, to understand the full detail of the signal of interest, to the level that they want or need to know at.
My Proxxon hobby tools come with a power supply with the DC symbol on it, and that's absolutely the correct description for their customers, some of whom will be very technical if they are using such tools. The output, of course, looks nothing like a flat line by any stretch (another example would be old-school battery chargers, I expect, from memory).
The manufacturer was still right to label it simply with a "DC" symbol with no further description.
I don't think every situation needs to have precise well-defined words (which might not even translate well to hundreds of languages), and will still not be as good as annotated diagrams and numbers/maths, specifications, etc.