All of that is under the umbrella term of ethical hacker. Black/grey/white hat are some very outdated and unclear terms, and also terms that non-tech people don’t really understand.

Ethical hacker is a term that lay people also understand and because of that it has replaced the rest of these terms.

(And also, “ethical hacker” encompasses both the grey and white hat. So it’s not an equivalent term to “grey hat”.)