~ The Whitehat Hacker ~
Refers to ethical hackers as well, as they (usually) only break into systems and pentest IF they have permission, thus they don't have a reason to do anything malicious except if it has been requested by f.ex. a contracting corporation (which is quite unlikely). These are also refered to as the good guys, as most of them makes proof of concept, consulting, etc. Which helps the internet to become more secure (even though their proof of concept are usually abused by f.ex. script kiddies). It should be said though, that ocasionally blackhats has been seen claiming they're whitehats, and also (of course) that script kiddies were whitehats.
~ The Gray/Greyhat Hacker ~
These guys, are also known as hybrid hackers as they are in between black- and white-hats. Usually, they don't hack for personal gain or have malicious intentions, yet they do break into systems without permissions ocasionally (or all the time) as well. The difference is they usually don't
have a purpose or interest in destroying other individuals data etc. It is though, important to keep in mind that they will not necessarily notify the system admin of a penetrated system, yet ocasionally they might notify the system admin if they feel like it. Some grayhats also prefer anonymity more than fast (and highly detectable) attacks as well.
~ The Blackhat Hacker ~
This is the type of hacker that hacks for usually personal gain, wether it is economical, political or just fun doesn't matter. There's no such thing as respect for authorities, loyality or morale (if there were, then they would be more near the grayhat area). In this case there's often found script kiddies claiming that they are pure blackhat, because it sounds cool, destroying and might work with non-hackers to induce a state of "awesome'ness", even though the real hackers would have no problem seeing that the person is just a script kiddy.
~ The Ghost Hacker ~
This type of hacker, doesn't exist as the person behind has hidden that identity so well he should never get caught. The reason why it's unlikely he would get caught is due to he's extremely well skilled and also very focused on what he is doing. The ghost hacker lives though, a double-life in the real world and also virtually. He has a job, usually an anonymous IT-job in the middleclass, which he does without any problems. He has a normal route and routine on the internet just as the others of us, but this whole identity is just an identity to hide his real intentions. In his other life, which NO ONE knows about, he has probably a room with seperate machines, which are quite stealthy. The last note about ghost hackers is they (usually) make big money on their things, and they might use a lot of time on doing the work with their contractors which are of course, hidden as well.
~ The Script Kiddie ~
A script kiddie is not a hacker. He doesn't have the required knowledge about computers, servers and networks, infact only very basical knowledge about protocols, if he even knows what a protocol is. He's usually not capable of programming anything, though he's usually found on forums where similar exchanges ignorance. These kind of guys usually claims they know a lot, even though they really don't thus they are also found striking very at very random targets, on todays internet usually google picks their targets for them by using googledorks which might have even been made by other more skilled hackers. Most script kiddies doesn't understand anything in depth, yet they think they know a lot cause they can do their advanced stuff on windows machines.