Bug: An ArcGIS Server WMS does not use the WMS operations when added directly in the ArcGIS Online Map Viewer
When adding an ArcGIS Server service published with WMS capability directly into the ArcGIS Online Map Viewer, the operations followed while working on the service correspond to the Map Server rather than WMS Server.
As per the standards of the ArcGIS Online Map Viewer's Java Script API, an ArcGIS Server service published with WMS capability behaves like a Map Server when added directly into it. This is due to the fact that when added directly into the Map Viewer, the Java Script API recognizes the service as an internal service and behaves in this way.
The workaround is to add the ArcGIS Server WMS Service as an item in ArcGIS Online and then add it into the ArcGIS Online Map Viewer.