Door closers have had many names over the years, work in many different ways, are fixed in many places, granted some control the closing and opening speed better than others but they all appear to use the same energy as was used to open the door to close it (so this must be a contributing factor in its description/definition). If it opens the door using a motor this is I believe is the exception and is rightly defined as a door opener, not a door closer.
Even if you consider the modern view of a door closer being surface mounted, is only single action and has an arm, why should that only that be thought of as a door closer? A floor spring for instance has an 'arm' (shoe/strap), can be single action (some are double action) are obviously mounted to a door and you can argue to the surface of the door if you take into account a single action shoe and how if fixes to the surface of the door.
A door closer can be simply called a overhead door spring
I hope you have enjoyed this post and as usual please feel free to leave a comment.