Primrose, that's pretty much spot on. To elaborate, grey market products are the same as their store bought counterparts but different markets have different selling prices. So if I'm Chanel I can sell a bottle of No. 19 to my U.S. distributor for $15 dollars but Chanel Zaire gets it for $10 to reflect the lower price the product commands in their area. Chanel Zaire, being no one's fool, realize that the U.S. distributor charges $30 per unit to retailers (department stores etc.) and sell their product to these same retailers for $25, a much better margin than the $15 dollars they got from their native retailers.
The issue is that Chanel Zaire doesn't own the distribution rights (or various equivalents) to the U.S. market and are infringing on the rights of the legitimate company and exposing C.Z. to possible law suits and even product seizure by Customs when their product makes it to the country. The product isn't illegal, hence not black market, but the retailer could be sued by the legitimate distributor for selling the unauthorized version.
Grey market products are extremely common; CVS pharmacies (a large U.S. pharmacy chain) was recently sued by a Davidoff distributor for selling grey market Cool Water after an inspection team's examination of 33,369 units in CVS's possesion determined that 16,600 (!) were gray market and 836 were counterfeits.