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Both high key and low key are lighting techniques that get mentioned a lot in studio photography workshops, video tutorials, etc. It's important to know the difference between them, but I also think they're poorly understood by a lot of people.
High key lighting is usually thought of as a lighting setup with a white background and well exposed model. It's partially true, but it's not the complete story. High key is not just about a white background, but about low contrast. This is actually the most important aspect to bear in mind when going for this technique. You need to tone down your contrast low enough to barely make the shape of the face and keep the photo from looking flat. It's a pretty forgiving type of lighting and it's often used by portrait studios and video bloggers for that reason.
Low key lighting on the other hand is a lot more dramatic and the reason for that are the much harsher shadows that come with the higher contrast. If you would have to point out the one major difference between the two, contrast would be it. Of course, to bring out more shadows and to exaggerate the sense of drama, a black or grey background will often be used with low key lighting. Needless to say, you shouldn't use it with non professional models or people who are less photogenic. It's not the most flattering type of light, but if you use it for the right kind of model or subject, you could end up with some powerful shots.
Here's a video from Adorama TV where the difference between the two is demonstrated in the studio.