For some reason (I can understand some of the logic, but not all of it) rommex or MC cable will be 12-3 for bk,rd,wht and green. However a 12-3 cord (being so, sjo,sow, sj etc) will only have bk,wht and green.
I think the practice comes back from the days when BX was used, 12-3 meant a bk,rd,white and an uninsulated ground. Same goes for rommex. So for both BX and Rommex 12-3 meant 3 insulated conductors and the ground was not insulated (as you have to have the EGC), whereas in a cord the ground was insulated. As we moved to MC with an insulated ground, I guess we still kept calling it a 12-3 even though it has now 4 insulated conductors.
However, that's is not an NEC issue. Same way NEC doesn't address whether you call it gutter, or troffer or wireway.
I am an electricain and I cannot find anywhere in the code NEC hand book that has a definition for a cable with conductors. Our boss says a 3 conductor cable with a ground has a total of 3 wires, two blacks and one green. I told him the cable should have 3 conductors plus a ground for a total of 4 wires. Is there a definition anywhere in the code book that would explain this? Thank-you, Ted