I can't answer how to spot a fake, but I do want to make sure we use the correct terms. A fake is an imitation phone made by someone else, being sold as if it were the real deal. I'm guessing this is what you are asking about.
A grey market item is a real, legitimate, item (The N10+ in this case), but being resold by an unauthorized seller in a location it wasn't intended for. What that means for phones is something like a legit U.S. version of the phone being bought here and sold to someone in Europe as new. The phone is real, never opened, never activated, and mint condition. The problem is it isn't set up for use in Europe, so you could run into problems with getting a tower connection, SMS support, and other unforseen issues. You also lose out on warranty support because there's no reliable chain of custody to insure the device wasn't tampered with. These are easily identified by their model numbers. There are several versions of the N10+, each with its own model number indicating the market it was meant for. You can see them all here.
https://m.gsmarena.com/samsung_galaxy_note10-9788.php
Grey market devices aren't inherently bad, so long as you understand what you're getting and the tradeoffs being made. Sometimes a reseller may offer a warranty to replace the lack of one from the manufacturer, but now you're relying on some no name company (or single person in some cases) to honor it if something goes wrong. They are also often sold at substantial discounts, which make the tradeoffs worth it to some people.
