WIRED has written an article defining “White Hat”, “Black Hat”, and “Grey Hat”. It’s incomplete and partisan.
Black Hats are the bad guys: cybercriminals (like Russian cybercrime gangs), cyberspies (like the Chinese state-sponsored hackers that broke into OPM), or cyberterrorists (ISIS hackers who want to crash the power grid). They may or may not include cybervandals (like some Anonymous activity) that simply defaces websites. Black Hats are those who want to cause damage or profit at the expense of others.
White Hats do the same thing as Black Hats, but are the good guys. The break into networks (as pentesters), but only with permission, when a company/organization hires them to break into their own network. They research the security art, such vulnerabilities, exploits, and viruses. When they find vulnerabilities, they typically work to fix/patch them. (That you frequently have to apply security updates to your computers/devices is primarily due to White Hats). They develop products and tools for use by good guys (even though they sometimes can be used by the bad guys). The movie “Sneakers” refers to a team of White Hat hackers.
Grey Hat is anything that doesn’t fit nicely within these two categories. There are many objective meanings. It can sometimes refer to those who break the law, but who don’t have criminal intent. It can sometimes include the cybervandals, whose activities are more of a prank rather than a serious enterprise. It can refer to “Search Engine Optimizers” who use unsavory methods to trick search engines like Google to rank certain pages higher in search results, to generate advertising profits.
But, it’s also used subjectively, to simply refer to activities the speaker disagrees with. Our community has many debates over proper behavior. Those on one side of a debate frequently use Gray Hat to refer to those on the other side of the debate.
The biggest recent debate is “0day sales to the NSA”, which blew up after Stuxnet, and in particular, after Snowden. This is when experts look for bugs/vulnerabilities, but instead of reporting them to the vendor to be fixed (as White Hats typically do), they sell the bugs to the NSA, so the vulnerabilities (call “0days” in this context) can be used to hack computers in intelligence and military operations. Partisans who don’t like the NSA use “Grey Hat” to refer to those who sell 0days to the NSA.
WIRED’s definition is this partisan definition. Kim Zetter has done more to report on Stuxnet than any other journalist, which is why her definition is so narrow.
But Google is your friend. If you search for “Gray Hat” on Google and set the time range to pre-Stuxnet, then you’ll find no use of the term that corresponds to Kim’s definition, despite the term being in widespread use for more than a decade by that point. Instead, you’ll find things like this EFF “Gray Hat Guide”. You’ll also find how L0pht used the term to describe themselves when selling their password cracking tool called “L0phtcrack”, from back in 1998.
Fast forward to today, activists from the EFF and ACLU call 0day sellers “merchants of death”. But those on the other side of the debate point out how the 0days in Stuxnet saved thousands of lives. The US government had decided to stop Iran’s nuclear program, and 0days gave them a way to do that without bombs, assassinations, or a shooting war. Those who engage in 0day sales do so with the highest professional ethics. If that WaPo article about Gray Hats unlocking the iPhone is true, then it’s almost certain it's the FBI side of things who leaked the information, because 0day sellers don’t. It’s the government who is full of people who foreswear their oaths for petty reasons, not those who do 0day research.
The point is, the ethics of 0day sales are a hot debate. Using either White Hat or Gray Hat to refer to 0day sellers prejudices that debate. It reflects your own opinion, not that of the listener, who might choose a different word. The definition by WIRED, or the use of "Gray Hat" in the WaPo article, are obviously biased and partisan.