Laszlo is correct in his fundamental terminologies. The term 
cable implies multiple strands. In the most general sense, a solid #12 would simply be a wire, and a stranded #12 would technically be cable. However, within the electrical world 
cable has a slightly more specific meaning. See definition 3a in the link above. 
 
With regard to ?sheath/jacket,? he is also correct. 
 
From (a very old copy) of ICEA S-95-658:
 
I note that while Article 338 is titled ?Nonmetallic-
Sheathed Cable,? the cable constructions are properly described as ?jacketed.?
 
ICEA S-95-658 has been absorbed into NEMA 70WC, but I don't believe the terminology has changed. I don?t have a current copy of either immediately available and what I do have is so old it doesn?t recognize the ?-2? markings for THHN, THWN, etc. It does however imply in Table 3-5 that, at the time at least, the nylon was considered part of the insulation system.
 
Additional Note: the definitions in the link above are consistent with Webster?s Collegiate Dictionary, 11th edition. From the NFPA Manual of Style:
 
 
Edit: italicized "
cable" in the second sentence