White hat hackers or more simply known as ethical hackers are those who put their skills to lawfully good use. These hackers are on the side of defense for corporations, companies or personal security through penetration testing, providing security consultation or participating in red teams to determine system defects.
Black hat or malicious hackers are people who use their tools with illegal and harmful intentions. These hackers are considered cybercriminals, deploying digital security attacks on companies to obtain employee and client personal information. They develop and release different forms of malware to damage devices or leak information for financial gain.
Between white and black, grey hat hackers are within the lines of morally right and wrong while still remaining safe legally. These hackers exploit vulnerabilities without personal and or corporate permission and will often report directly to the victim or to social media in hopes of motivating a patch. A great example of grey hat hackers is the Anonymous group. Their actions are often seen as controversial however within their morals they believe that what they are doing is correct and just.
Also a fitting title for the Anonymous group, Hacktivists perform digital breaches for social and or political awareness. Its seen as a form of digital protesting.
State or nation sponsored hackers are big groups of hackers that are employed by the government to attack opposing governments for geological advancement and benefit.
Cyberterrorists are motivated by political and violent ideology to inflict. They do this through cyber attacks, targeting infrastructure, and collapsing essential services.
Insider threats are vulnerabilities that were exploited by company employees, partners and or contractors. They do this with the intention of revenge, greed, whistleblowing or coercion. This is done by taking the authorization for granted, and using the tools provided by their employer and turning it against them.