I sort of understand the graphics layer as being for runtime transient rendering, while the feature layer is for persistable business specific elements.... How does the Operational Layer fit / relate to either of these two ?
OperationalLayers is the collection of layers in the map containing your feature layers, raster layers, map image layers, etc. It's a term we inherit from the ArcGIS geoinformation model and you will see used across the ArcGIS platform.
There is an important difference between graphics overlays in the view overlays collection and feature layers in the operational layers collection: when you save the map, graphics overlays are not saved. If you want to create those kind of 'in memory' objects and save them with the map then I recommend considering the FeatureCollectionLayer.
For more info see:
- operationalLayers | ArcGIS for Developers (Webmap spec)