Grey hat hackers are those who do not identify with black hats or white hats. Their lot differs in hacking technique and in disclosing findings. Usually, grey hats do not hack to gain notoriety or money unlike the black hats but are quite ready to do something illegal to attain their goal in exploiting security holes or gaining information.
Moreover, grey hats would not necessarily let the companies know at once, as opposed to white hats, but will neither endeavor to conceal it for gaining money. Their usual course of action seems to be exposing it to the media and public first.
Similar to white hats, grey hats’ usual intention is to test and secure rather than to simply damage and steal (but differs from the former as they do not completely disclose their dumps).
Hacktivists are also commonly categorized as grey hats.
Hass and Associates Cyber Security: Grey Hat