What is the name of a portion of video between camera changes?
It sounds like you are describing shots.  A scene is composed of one or more shots covering a consistent location and time.  Each separate clip within the scene is simply referred to as a shot.  The shot changes any time that the camera position is moved.  Technically, if you are on a close up shot and cut to a wide angle and then cut back to a close up, they would both be part of the same close up shot if they were from a continuous clip, but I've never heard any other term applied to the smallest unit of continuous video.

If the shots transition directly from one to the other without any interlude, this is referred to as a cut.  The term comes from the film days when one would cut the film and splice it together with the first frame of the next scene.