As an owner of a genuine grey-market vehicle, I can say that the term refers to cars that were models that were not marketed in this country by the manufacturer/dealer network. So bringing in a Volvo 240 (or other make/model) from Europe doesn't count if you could buy the same car from a dealer here in the states.

The grey-market car I own is a 1984 Mercedes-Benz Gelaendewagen, a 280GE (W460 chassis, M110 engine) -- it was imported by a Registered Importer in New Mexico, named Europa Int'l. And it wasn't until nearly the year 2000 that M-B dealers in this country started selling this car themselves, called the GWagen here.
A R.I. is a company that not only brings it into the country (either on speculation, or for a customer that orders it) and then subjects it to sometimes considerable rebuilding and modification to make it comply with some (but not all) U.S. regulations. The R.I. has to be licensed by both the U.S. DOT and EPA, to ensure that the modifications were done right. And the owner(s) subsequently have to keep the certifying documents (issued by the DOT and EPA) to submit to state Motor Vehicle agencies when they get their titles and registrations, plates, etc.; without the documents, such a grey-market vehicle cannot be licensed to be operated on public roads.

Until about 1986 or so, U.S. citizens could, one time in their lifetime, bring such a new car into the country (through a R.I., to be modified) and subsequently have it road legal. This is why most grey-market cars are at least model year 1986 or older.
[BTW, this whole discussion applies to the original gey-market importation of new cars -- old, used cars that are imported are subject to different regulations that I'm not familiar with.]

After ~1986, the rules for grey-market cars becomes murky, and essentially impossible to navigate. Manufacturers/dealers in this country would rather have you buy a car (built to U.S. specs as if it were sold in the U.S.) through their own "overseas" sales network, and the U.S. government would rather not address the concerns of cars that do not comply with U.S. EPA and DOT regs. The pre-'86 grey-market rules did not require full compliance, but only certain select things -- e.g., regarding DOT's purvue in crash safety, the model didn't have to be crash tested, but it had to have door beams installed; and other things like that. However, certain other features, such as a unique light switch*, did not have to be converted to U.S. specs.
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* My headlight switch allows me to turn on the lights on one side, or the other side, of the car, if I wish, rather than on both sides. Can you imagine the feds allowing this on U.S. cars?
BTW, the reason is that it allows, when parking on the side of the road (e.g., in narrow streets in European cities), the lights to be lit on only the traffic side of the car to halve the rate of battery drain.
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Hope this helps.

I just called Crutchfield and they don't have radios that play in anything other than English. I think it would be cool to have something exotic like that in my car.