Point of view shot

A point of view shot, also known as POV shot, is a short film scene that shows what a character is looking at, its represented through the camera. It is normally shown by showing that the character is looking at something and then in the next shot showing what the character is actually looking at. 

A POV shot doesn't always need to be a direct shot which is just a shot of what the character is looking at it could be filmed as an over the shoulder shot.

Cutaways

A cutaway is a short that's usually something different to what the current action is. It could be a different subject, a close up of the subject (e.g. the subjects hands) or just about anything else.  This editing technique could also be used as a "buffer" between shots (to help the editing process), or to add interest/information.

Here is an example of a cutaway shot.