To answer my own question, it seems the correct name for the current inch-based (as opposed to metric) thread standard is "Unified" or "Unified Standard," which includes Unified Standard Fine and Unified Standard Coarse. I am assuming that the agreed Unified standards specify head sizes as well; if that is true, then one should refer to wrenches and sockets that fit Unified bolts and nuts as "Unified" or "Unified Standard" wrenches and sockets. I assume "Unified" refers to fact that, by adopting its parameters, the U.S., Canada, and English have agreed to a single standard (for pitch, diameter, fit, etc.).
I am not sure where "SAE" fits in, although the Society did set some thread standards before, which may have been adopted in the Unified system. "SAE" hardly ever cropped up in the quick and dirty research I did, which included a quick review of Carroll Smith's classic book on nuts and bolts (which he wanted to name "Screw to Win," by the way).
No one refers to wrenches and sockets as "Unified" either.
Snap-On, in their catalog, I think distinguishes these tools from their metric equivalents by simply referring to them as "inches." Proto seems to use "standard," which I suppose is linked to "Unified Standard." "Standard," however, is a bit confusing, as metric is the new "standard."
On my tool cabinets, I simply used "sockets, inches" as against "sockets, metric." This makes it simpler for friends who come help with the work know where to find and store things.
As in many things, I could be completely wrong here, so please correct me.
Regards,
Andres