Relativity cares not where mass comes from.
I like this, and makes me ask, for more door-opening. Clearly this question is covered in the “usually”'s you state, so here’s one more “usual,” in naive intuitive understanding:
I slam into something “massive” or don’t fall through chairs, e.g., because the electrodynamic forces are the gatekeepers at our level. So I’ve been told (in SD and elsewhere); just as Einstein physics elaborates Newtonian under changed circumstances, when does the “elaboration” it’s-nuclear-binding-not-electrodynamic kick in?
PS: And try not to say “at the nuclear level.” Or if you do, add a smiley.
The main differences between the strong force and electromagnetism (at least, the ones relevant for this question) are that, first, the strong force has a much shorter range, and second, over the range over which it works, it’s much stronger than electromagnetism (hence the name). So if you have two hadrons (particles subject to the strong force, basically those made up of quarks), if they’re far apart, the dominant force between them will be electromagnetic, and if they’re close together, the dominant force will be the strong force. There is of course a distance where this change happens, at which both forces are about equally relevant: This distance is a few times the diameter of a proton.
I’d be careful about using the term “relativistic mass” as perversely it usually means something different to the usual definition of mass in relativity. The mass of the system should be seen as a fundamental property of the system in special relativity.
I’ve seen Chronos almost lose it commenting on that term as employed by hoi polloi.
I’m actually very calm when I type about that subject, though I realize that might not come through in text. I mean, yeah, it’s frustrating, but it’s a frustration I’m used to, and the cause of the problem is never the people I’m addressing.