A grey market or gray market, also known as parallel market, is the trade of a commodity through distribution channels which, while legal, are unofficial, unauthorized, or unintended by the original manufacturer. - Wikipedia
Generally speaking, the item you're purchasing is new as advertised and sold legally by a vendor. The difference is that the product is not being sold through an authorized reseller. An authorized reseller has a formal agreement with a manufacturer to sell their product, usually at preset prices. In return the reseller might gain access to quantities and discounts. This practice allows the manufacturer to control the market pricing of their product where otherwise vendors might set pricing as they so desire (free market and all), as well as ensure the quality/validity of the vendors and distribution chain/channels.
Unauthorized resellers engage in the practice of a parallel market to make money off the difference in regional pricing. If a given product is cheaper in one market, someone could buy quantities of the product in that one market and sell it for a higher margin in a region where that market's pricing is higher.
Cal Civ Code § 1797.8 defines grey market goods as consumer goods bearing a trademark and normally accompanied by an express written warranty valid in the United States of America which are imported into the United States through channels other than the manufacturer's authorized United States distributor and which are not accompanied by the manufacturer's express written warranty valid in the U.S. - USLegal
Your mileage will definitely vary, so we'd suggest erring on the side of caution. We'd caution against gray market purchases of larger more expensive items that can be expensive to fix. Some simpler and cheaper tech items you might not get as big of a price break on with gray market purchases but it's also not as big of a deal if you have to repair it on your own dime, so it might be worth it to you. Just watch your rear, and know that you might not have the manufacturer behind your back on this one.