"Digital camera" usually refers to a digital still camera; these are similar to 35mm snapshot cameras, except that they contain no film. Some digital still cameras allow you to capture short (under 30 second) clips of audio as well, and some can be connected to televisions in order to preview the pictures in the camera.
A "digital video camera" is similar to a regular camcorder or video camera, except that it stores the recorded video in a digital (as opposed to analog) format. This results in video which can be duplicated many times or copied directly into a computer without any additional loss of image quality.
A "DV camera" is a specific type of digital video camera that shoots in the "DV" format. This is the same format that editing software uses, therefore video on a DV cassette doesn't lose any quality when captured directly to these programs.
Most popular consumer DV video cameras use Mini DV tapes. Mini DV tapes capture the same fine-quality video as their larger industrial counterparts and are relatively inexpensive.