Yes,there's somewhat of a confusion with terms:"Set" can be used as a general term for any Set-,or Struck tool;but also (as in this case) for a tool that is used to Set the steel Down in an abrupt,localised manner.
The difference would be that the Set-hammer's face is small and concentrated,limited in it's area in order to transfer the impact of the blow.
Conversely,a flatter is extended into a wide flange covering a large area,that's so that the impact gradually lessens and dissipates toward the edges,it is that which allows the "flatting" blows to blend together to create a continuous surface,or the edges will mar the work.
(i'm not an expert either....the more time one puts in at the anvil the less of an expert one becomes.....