generally, NOS steel parts will have a lacquerised grease coating, grease that has hardened, patchy and as you say possibly bits of paper on. there may also be signs of light rust if not fully protected. this is hard to replicate .
I would think the number of "old" bike shops is limited now so their stock will run out. Ive been to a few auctions of local bike shops where the "old stuff" is noticably missing from the stock on offer.
I would suggest NOS would nowadays be 1980's to 90's made parts.
With the Indian's making more and more parts now I suspect the term will appear more often.
I remember Fluff Brown, (FBAJS) went on holiday to America in the nineties, while there he managed to collect himself a container or two full of his old stock from American AJS dealers icluding complete bikes.