The substantive difference I see is that "scriptwriting" is actually more restrictive than "script".
In film, what a person writes is called a "spec script", what the director uses is called a "shooting script".
See for example: 5 Key Differences Between Spec and Shooting Scripts
In particular and most important,
In spec scripts it’s never a good idea to include camera directions (PAN, DOLLY, TILT UP, ZOOM IN ON, CRANE UP, etc.). It’s the Director’s job to interpret your screenplay and come up with their own shots.
That isn't it, the spec script does NOT contain scene numbers, the shooting script does. And there may be other notes in the shooting script as well, and other sections. For example, the author of a spec script does not write how the title sequences will work, or even suggest it. Those are marks of an amateur.
Our current distinctions may not be clear, but I think "scriptwriting" may be questions about crafting a spec script (to be sold) while "script" might question the meaning of notations, acronyms, or symbols or special effect notes used by directors in a shooting script.
I don't know but a similar distinction might apply to Stage Play scripts, the director may add directorial notes to his copy of the script (although camera angles aren't needed of course, certain stage directions seem likely).