I have never had direct access to any Esri product, but I have written code that has interacted with ArcGIS Server, with layers that have the word "MapServer" prominently in the URL and in the JSON they provide.
But what exactly is "MapServer" (not to be confused with the other MapServer)? Is it a product? Is it just a protocol, akin to WMS? Is there actually any stand alone service called MapServer, or is it (as I suspect) just a name given to the protocol used to access generated raster map images?