Here are some brief definitions to help keep this stuff in the right context.

I guess you could use hacker or cracker, depending on which term you prefer.

Blackhat: |Insert Preferred term here| who attempts to gain access to systems and information with the intent to steal, deface, destroy, sabotage, or otherwise perform a malicious act.

Greyhat : |Insert Preferred term here| who attempts to gain access or information which is usually used to find and fix vulnerabilities without the permission or knowledge of the system owner. Usually does not involve malicious intent. The actions and methods used may be considered malicious by the system owner. The actual intent of the greyhat is uncertain, or grey, hence the use of the term.

Whitehat: |Insert Preferred term here|, usually a system or security administrator or consultant, who uses the many of the same methods and tools Blackhats and Greyhats use, but with the intent to find and fix vulnerabilities and otherwise secure systems they control against malicious attackers. The intentions of Whitehats are not malicious. These actions are always performed with permission from the system owner.