Do video cameras have the image sensors cameras have?
I really don't know what I'm talking about, so if the answer was explained, I would really appreciate it.
Yes. Digital video cameras use these sensors, usually CCDs but CMOS too. These are the same designs use for still cameras but with less pixels, since even HD footage only needs 2 MP. For HD cameras, the shape of the sensor is often different to match the 16:9 aspect of widescreen footage.
The major difference you will encounter are cameras labelled as 3 CCD. Again this is the same type of sensor but there are 3 of them, one for each of red, green and blue. Special prisms are used to divide incoming light and reflect it towards each sensor. On a conventional digital camera, colors are almost always divided between adjacent pixels using a Bayer filter. There are some Sigma cameras which use special Foveon sensors which capture different colors in layers instead.