What is the distinction between white hat and black hat hackers?

"Black hat hackers find vulnerabilities to help problems, white hat hackers are trying to unlawfully acquire information."

"Black hat hackers write fixes for security problems, white hat hackers write exploits."

"White hat hackers try and write fixes for security problems, black hat hackers write exploits"

"White hat hackers find vulnerabilities to help problems, black hat hackers are trying to unlawfully acquire information."