Standards for map services were set by OGC and ISO, called WMS and WMTS. Producing map images on the web from a cartographic image in a GIS application is called "publishing". Making a web "map" in the broader sense of constructing data representations for Storytelling or Geo-gaming is still under development. It requires a mix of applying the map Design principles and Graphic presentation techniques, possibly in combination with software scripting.
In progress (GI-N2K)