"Hole in the wall fire" , If you mean a fire where the flue goes horizontally through the wall to outside this is called a balanced flue fire and can be fitted on nearly any external wall. An inset fire can only be fitted in a builders opening of an existing chimney breast or flue.
an inset fire is just what is says "inset" you're run of the mill living flame job that sits inside the chimney or flue. however some hole in the wall fires,that usually means they are raised up off the floor,can also take an inset fire.complicated innit